Find the area of AON | Mathematics | Page 1

tight blaze Apr 3, 2024, 11:47 PM

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Need to find the area of AON.

celest rampartBOT Apr 3, 2024, 11:47 PM

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tight blaze Need to find the area of AON.

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tight blaze Apr 3, 2024, 11:51 PM

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Find the area of AON

mint crater Apr 3, 2024, 11:52 PM

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tight blaze Need to find the area of AON.

Well what 2 triangles can we prove similar

tight blaze Apr 3, 2024, 11:53 PM

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None.

mint crater Apr 3, 2024, 11:53 PM

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Looking at angle properties in parallel lines, since this is a square

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I would do AON and BOC

tight blaze Apr 3, 2024, 11:54 PM

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But they don't look similar

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Am i blind

mint crater Apr 3, 2024, 11:54 PM

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You can't prove similarity by looking lol

tight blaze Apr 3, 2024, 11:54 PM

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Ok

mint crater Apr 3, 2024, 11:54 PM

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Do you know the vertical angles theorem

tight blaze Apr 3, 2024, 11:54 PM

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Let me check the theorem rq

mint crater Apr 3, 2024, 11:55 PM

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You need to know 2

tight blaze Apr 3, 2024, 11:55 PM

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Ohhh

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Yes

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Yeahp

mint crater Apr 3, 2024, 11:55 PM

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Vertical angles theorem and alternate interior angles

tight blaze Apr 3, 2024, 11:55 PM

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Yeah i know tjat

mint crater Apr 3, 2024, 11:55 PM

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Ok

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So after finding a pair of vertical angles and another pair of alternate interior angles

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You can prove the two triangles similar

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And we have a side on both

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So you can tell me the ratio

tight blaze Apr 3, 2024, 11:57 PM

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Hm

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We can safely say that

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These are 45 degrees

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mint crater Apr 3, 2024, 11:58 PM

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Ok

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And now we can prove the pair of vertical angles with AON and BOC

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Do you see those angles

tight blaze Apr 3, 2024, 11:59 PM

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You mean these?

mint crater Apr 4, 2024, 12:00 AM

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Yes

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So we can prove triangle AON and triangle BOC similar right

tight blaze Apr 4, 2024, 12:00 AM

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Yeah

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Oh

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So you mean to say that,

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2/3a / ON = BO / a ?

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Or is it other way around

mint crater Apr 4, 2024, 12:02 AM

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Well they are just similar that the side lengths of AON are 2/3 the corresponding side lengths of BOC

tight blaze Apr 4, 2024, 12:02 AM

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Rightt

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You're cooking

mint crater Apr 4, 2024, 12:03 AM

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Lmao

tight blaze Apr 4, 2024, 12:04 AM

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Is it other way around

mint crater Apr 4, 2024, 12:04 AM

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Ok so we find the area of AON in terms of a right

mint crater Apr 4, 2024, 12:04 AM

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tight blaze Or is it other way around

Yea

tight blaze Apr 4, 2024, 12:04 AM

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2/3a /AO = OC / a

mint crater Apr 4, 2024, 12:05 AM

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tight blaze 2/3a /AO = OC / a

No

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The second should be flipped

tight blaze Apr 4, 2024, 12:05 AM

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a / OC?

mint crater Apr 4, 2024, 12:05 AM

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Yea

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Now cross multiply

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And verify

tight blaze Apr 4, 2024, 12:06 AM

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Okay so

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We got

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AO * a = 2/3a * OC

mint crater Apr 4, 2024, 12:06 AM

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Alright so we are trying to find the area of AON right

tight blaze Apr 4, 2024, 12:06 AM

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Yeah

mint crater Apr 4, 2024, 12:07 AM

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So

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Let’s draw a line straight down from O to the line AD

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And it is perpendicular to OD and makes a right angle

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Call this point F

tight blaze Apr 4, 2024, 12:08 AM

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Ok

mint crater Apr 4, 2024, 12:08 AM

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Tell me when you are finished with that

tight blaze Apr 4, 2024, 12:08 AM

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I did

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It

mint crater Apr 4, 2024, 12:08 AM

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Ok

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So we calculate the area of AON by AN * OF * 1/2 right

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Where * is multiplication

tight blaze Apr 4, 2024, 12:09 AM

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Mhm

mint crater Apr 4, 2024, 12:09 AM

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Ok

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So we have AN = 2/3a right

tight blaze Apr 4, 2024, 12:10 AM

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True

mint crater Apr 4, 2024, 12:10 AM

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And we draw a line straight through FO to the other side

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That would be the altitude of BOC

tight blaze Apr 4, 2024, 12:10 AM

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Mhm

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Done

mint crater Apr 4, 2024, 12:11 AM

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Ok

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So let’s call the point on the other side G right

tight blaze Apr 4, 2024, 12:12 AM

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Yes

mint crater Apr 4, 2024, 12:13 AM

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Because of our similarity laws we know OF = 2/3 OG

tight blaze Apr 4, 2024, 12:13 AM

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Okay

mint crater Apr 4, 2024, 12:13 AM

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And OG + OF = a

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So we can substitute

tight blaze Apr 4, 2024, 12:13 AM

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2/3 OF + OF = a?

mint crater Apr 4, 2024, 12:14 AM

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Yup

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Solve for a in terms of OF

tight blaze Apr 4, 2024, 12:14 AM

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5/3 OF = a

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OF = 2/5

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I meant 2/5

mint crater Apr 4, 2024, 12:15 AM

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Ok

tight blaze Apr 4, 2024, 12:15 AM

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I got it

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2/5 * 2/3

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That's the answer

mint crater Apr 4, 2024, 12:15 AM

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Don’t forget the 1/2 and the a

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Stuff

tight blaze Apr 4, 2024, 12:16 AM

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Oh

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Yeah

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2/5 a * 2/3 a * 1/2

mint crater Apr 4, 2024, 12:16 AM

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Yes

tight blaze Apr 4, 2024, 12:17 AM

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2/15 a

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Final answer

mint crater Apr 4, 2024, 12:17 AM

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No

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A is multiplied twice

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Also I wrote an expression wrong my bad

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You still got it right though

tight blaze Apr 4, 2024, 12:18 AM

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Oh erigjt

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2/15a^2

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Thats it right

mint crater Apr 4, 2024, 12:18 AM

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Yes

tight blaze Apr 4, 2024, 12:18 AM

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Let me check the answer rq

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Yup

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Thats it

mint crater Apr 4, 2024, 12:19 AM

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Alright

tight blaze Apr 4, 2024, 12:19 AM

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Thank you california

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You cooked once again

mint crater Apr 4, 2024, 12:19 AM

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Bro thanked a state

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Np

tight blaze Apr 4, 2024, 12:19 AM

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Whatd you want me to thank

mint crater Apr 4, 2024, 12:19 AM

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The jumping bean

tight blaze Apr 4, 2024, 12:19 AM

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A jumping bean

mint crater Apr 4, 2024, 12:19 AM

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Lol

tight blaze Apr 4, 2024, 12:20 AM

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No thanks i'll thank the state for their hard work

mint crater Apr 4, 2024, 12:20 AM

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Do you know how to close the post

mint crater Apr 4, 2024, 12:20 AM

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tight blaze No thanks i'll thank the state for their hard work

Yo

tight blaze Apr 4, 2024, 12:21 AM

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Hold on

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Im re-reading

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The post

mint crater Apr 4, 2024, 12:21 AM

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Ok

tight blaze Apr 4, 2024, 12:21 AM

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Then i have to nominate u

mint crater Apr 4, 2024, 12:21 AM

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Same I need to learn

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What I did good

tight blaze Apr 4, 2024, 12:22 AM

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Are u planning on becoming

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A teacher or

mint crater Apr 4, 2024, 12:22 AM

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No

tight blaze Apr 4, 2024, 12:22 AM

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A professor

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Oh

mint crater Apr 4, 2024, 12:22 AM

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I’m just having fun

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I’m bad at geometry so thanks for helping man

tight blaze Apr 4, 2024, 12:22 AM

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You having fun saved me a lot of torture lol

mint crater Apr 4, 2024, 12:23 AM

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tight blaze You having fun saved me a lot of torture lol

Lol

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Caught another mistype Lol

tight blaze Apr 4, 2024, 12:25 AM

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Alr

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Lmk if you want me to

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Close the post

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I've pretty much wrote down

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All the important stuff

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To memorize

mint crater Apr 4, 2024, 12:25 AM

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tight blaze 5/3 OF = a

Yes this is supposed to be 5/2 OF

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Alright you can close

tight blaze Apr 4, 2024, 12:26 AM

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Oh

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No

mint crater Apr 4, 2024, 12:26 AM

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What

tight blaze Apr 4, 2024, 12:26 AM

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Wait

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But

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Isn't it supposed to be

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5/3

mint crater Apr 4, 2024, 12:26 AM

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I mistyped the last thing

tight blaze Apr 4, 2024, 12:26 AM

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Since

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Oh

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LOL

mint crater Apr 4, 2024, 12:26 AM

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I said OG = 2/3 OF

tight blaze Apr 4, 2024, 12:26 AM

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and i still managed to write it correctly

mint crater Apr 4, 2024, 12:27 AM

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Well

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That good

tight blaze Apr 4, 2024, 12:27 AM

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Wait hold on

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I think i didnt

mint crater Apr 4, 2024, 12:27 AM

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Cuz that means you know what you are doing

tight blaze Apr 4, 2024, 12:27 AM

#

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I didn't write it correctly

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Indtead of

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OF

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it should've been OG then

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Or

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Vice versa

mint crater Apr 4, 2024, 12:28 AM

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Well

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My bad man

tight blaze Apr 4, 2024, 12:28 AM

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Nah its fine

mint crater Apr 4, 2024, 12:28 AM

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But hopefully this helped

tight blaze Apr 4, 2024, 12:28 AM

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It did it did

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Imma keep this post up for a sec

mint crater Apr 4, 2024, 12:29 AM

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It’s your decision

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Keep it open as long as you need

tight blaze Apr 4, 2024, 12:32 AM

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Somehow,

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We managed to get the right

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Answer

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With wrong steps

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To make the whole thing correct it should've been OG = 2/3 OF

mint crater Apr 4, 2024, 12:32 AM

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Well it’s not wrong steps

tight blaze Apr 4, 2024, 12:33 AM

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But it doesnt

mint crater Apr 4, 2024, 12:33 AM

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Just a mistype

tight blaze Apr 4, 2024, 12:33 AM

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I guess so

mint crater Apr 4, 2024, 12:33 AM

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tight blaze To make the whole thing correct it should've been OG = 2/3 OF

Nah other way

tight blaze Apr 4, 2024, 12:33 AM

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Yeah

mint crater Apr 4, 2024, 12:33 AM

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OG is the bigger side

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Im curious as to how you guys are taught to approach this problem

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What does your teacher say

mint crater Apr 4, 2024, 12:36 AM

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tight blaze Yeah

Because you seemed to know the theorems but not how to apply them

tight blaze Apr 4, 2024, 12:37 AM

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I'm as dumb as a rock when it comes to applying stuff lol

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Plus its

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3 am?

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Haha

mint crater Apr 4, 2024, 12:37 AM

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Holy bro

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Go sleep

tight blaze Apr 4, 2024, 12:37 AM

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Cant

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Math early

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Have to do the rest 8 problems

mint crater Apr 4, 2024, 12:37 AM

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Ok

tight blaze Apr 4, 2024, 12:37 AM

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Nvm its 10

mint crater Apr 4, 2024, 12:37 AM

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If you think you may need help with any of them keep this thread open

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But good luck

tight blaze Apr 4, 2024, 12:38 AM

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Alr I am grateful for the help

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Got the same situation here

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Just need to find OF

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And we're good to go

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The answer is

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3/14a^2

fallow heron Apr 4, 2024, 12:58 AM

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this is a square right?

mint crater Apr 4, 2024, 12:59 AM

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fallow heron this is a square right?

Yup

tight blaze Apr 4, 2024, 12:59 AM

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Yes

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All sides are equal to one another

fallow heron Apr 4, 2024, 12:59 AM

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i would just hard coordbash this /hj

mint crater Apr 4, 2024, 1:00 AM

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Idk if op knows coordbash though

tight blaze Apr 4, 2024, 1:00 AM

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Yeah, not tought

mint crater Apr 4, 2024, 1:00 AM

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tight blaze Yes

Hey do you know how to solve by assigning coordinates and calculating slope

tight blaze Apr 4, 2024, 1:00 AM

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If used I'll be accused of cheating

mint crater Apr 4, 2024, 1:00 AM

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Damn

tight blaze Apr 4, 2024, 1:01 AM

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Some learning methods are bad

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But that's how it is

mint crater Apr 4, 2024, 1:01 AM

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They don’t allow you to use thought?

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Only formulas is crazy

tight blaze Apr 4, 2024, 1:01 AM

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Nope.

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Formulas

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Strictly

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And maybe some logic

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Whats more infuriating

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We just went through a similar

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Problem

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Except this one is just a kick below the belt

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Isn't it possible to just

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Find the area of ADK

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And the area of BDC

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And just subtract

mint crater Apr 4, 2024, 1:04 AM

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Wait

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What area are we trying to find

tight blaze Apr 4, 2024, 1:04 AM

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AOD

mint crater Apr 4, 2024, 1:06 AM

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I would do BAD - BOA

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Looks the easiest

tight blaze Apr 4, 2024, 1:06 AM

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What's BOA tho

mint crater Apr 4, 2024, 1:07 AM

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Can’t we use the 3/5a from the altitude

tight blaze Apr 4, 2024, 1:07 AM

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I guess so

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We got

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a^2/2 - 3/10a^2

mint crater Apr 4, 2024, 1:08 AM

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First one you forgot the 1/2

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Yeah

tight blaze Apr 4, 2024, 1:09 AM

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2a^2 / 10

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a^2 / 5

mint crater Apr 4, 2024, 1:09 AM

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Ok

tight blaze Apr 4, 2024, 1:10 AM

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Okay nah im brute forcing and just pulling a lazy trick

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Gonna write an answer without steps

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See how she likes it

mint crater Apr 4, 2024, 1:10 AM

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What

tight blaze Apr 4, 2024, 1:10 AM

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That wasnt

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The answer

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The correct one

mint crater Apr 4, 2024, 1:10 AM

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Let me coordbash one sec

tight blaze Apr 4, 2024, 1:10 AM

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Alr

mint crater Apr 4, 2024, 1:13 AM

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Ok

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I got my answer again

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Want me to explain

tight blaze Apr 4, 2024, 1:13 AM

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Yes please

mint crater Apr 4, 2024, 1:13 AM

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Ok

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Gimme 1 sec so I can type faster

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ok im back

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ok so I will give coordinates for the vertices

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A = (0,0) ---> B = (0,3) ---> C = (3,3) ---> D = (3,0)

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K = (3,2)

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we need to find O and F

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do you understand?

tight blaze Apr 4, 2024, 1:17 AM

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So far

mint crater Apr 4, 2024, 1:17 AM

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ok

tight blaze Apr 4, 2024, 1:17 AM

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Yes

mint crater Apr 4, 2024, 1:17 AM

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so first we calculate the equations for the lines AK and BD

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so we have the points

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A is (0,0)

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and K is (3,2)

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so the slope of AK is (2-0)/(3-0)

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= 2/3

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nothing else

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so the equation of line AK is y = 2/3 x

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and we have

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B = (0,3) and D = (3,0)

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slope is (0-3)/(3-0)

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= -1

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so we have y = -x

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and then we need to add 3 to get the correct y value

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so the equation for line BD is y = -x + 3

mint crater Apr 4, 2024, 1:20 AM

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tight blaze Yes

do you understand so far?

tight blaze Apr 4, 2024, 1:20 AM

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Yes

mint crater Apr 4, 2024, 1:20 AM

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ok

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so we need to calculate their intersection to find the coordinates of O

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so since they are both equal to y

tight blaze Apr 4, 2024, 1:21 AM

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We

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Equal them

mint crater Apr 4, 2024, 1:21 AM

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we say y = -x + 3, and y = 2/3x

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yea

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and you get -x + 3 = 2/3x

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5/3x = 3

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x = 9/5

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so that is the x coordinate

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we need the y

tight blaze Apr 4, 2024, 1:21 AM

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Ahuh

mint crater Apr 4, 2024, 1:21 AM

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which is 2/3 of the x

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so y = (2/3)(9/5)

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= 6/5

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so the height of AOD is (6/5)

tight blaze Apr 4, 2024, 1:22 AM

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6/5*1/2

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*a

mint crater Apr 4, 2024, 1:22 AM

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dw about the a yet

tight blaze Apr 4, 2024, 1:22 AM

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Are we supposed to leave

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a

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As it is

mint crater Apr 4, 2024, 1:22 AM

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so we have 3 * 6/5 * 1/2

tight blaze Apr 4, 2024, 1:23 AM

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Oh

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18/10

mint crater Apr 4, 2024, 1:23 AM

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tight blaze Are we supposed to leave

ill input it later

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i plugged in a as 3

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so thats 9/5

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right

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1/5 a^2 = (3^2) * 1/5

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= 9/5

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same answer

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therefore

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the answer should be 1/5 a^2

tight blaze Apr 4, 2024, 1:23 AM

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Guess that's the true answer

mint crater Apr 4, 2024, 1:24 AM

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how many do you have left

tight blaze Apr 4, 2024, 1:24 AM

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I'll write that down and go to sleep

mint crater Apr 4, 2024, 1:24 AM

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ok

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definitely

tight blaze Apr 4, 2024, 1:24 AM

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A lot but i'll just do it tomorrow

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Tyy

mint crater Apr 4, 2024, 1:25 AM

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np

mint crater Apr 4, 2024, 6:19 PM

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tight blaze Guess that's the true answer

Curious as to what your teacher said though or what your classmates got

tight blaze Apr 4, 2024, 6:19 PM

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I have the step by step explanation

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Managed to do the other 5 problems

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By my self

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With correct answers

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Im proud of myself :3

tight blaze Apr 4, 2024, 6:22 PM

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mint crater Curious as to what your teacher said though or what your classmates got

Oh right i forgot

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She said there illogical

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Info

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In it

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It aint right, the problem itself is not right

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@mint crater

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So avoid it entirely

mint crater Apr 4, 2024, 7:02 PM

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tight blaze Managed to do the other 5 problems

Nice

tight blaze Apr 6, 2024, 10:28 AM

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@mint crater

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Are you good in

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Algebra

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By any chance

mint crater Apr 6, 2024, 10:50 AM

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What do you need help with

mint crater Apr 6, 2024, 10:53 AM

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tight blaze Algebra

Post the problem

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And if I can't help start a new thread

tight blaze Apr 6, 2024, 10:54 AM

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mint crater Apr 6, 2024, 10:54 AM

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,rotate

tight blaze Apr 6, 2024, 10:55 AM

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Solve -3|x|+2|x-5| if

echo vectorBOT Apr 6, 2024, 10:55 AM

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mint crater Apr 6, 2024, 10:57 AM

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tight blaze Solve -3|x|+2|x-5| if

If?

tight blaze Apr 6, 2024, 10:57 AM

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1<_ x <_ 3

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I meant to write

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< _

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Less or equal

mint crater Apr 6, 2024, 10:59 AM

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Wdym solve

mint crater Apr 6, 2024, 11:01 AM

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tight blaze Solve -3|x|+2|x-5| if

Do you know how your teacher or someone did it

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Because

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We are just given an inequality equal to nothing

tight blaze Apr 6, 2024, 11:01 AM

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Cant seem to remember

mint crater Apr 6, 2024, 11:01 AM

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And a random range

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I don't think you can solve that

tight blaze Apr 6, 2024, 11:01 AM

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Yeah i'll ignore that one ig

tight blaze Apr 8, 2024, 10:51 PM

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+close

#Find the area of AON