Geometry question

[river shoal]

Does anyone know how to do this? I'm really confused

[karmic lily]

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[jovial valve]

[river shoal]

Is it that bad?

[jovial valve]

P infinity is gonna be a circle

just gotta find its radius

[jovial valve]

it is by the looks of it

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yeah

oof well

[jovial valve]

but its gonna have a neat solution for sure

Ooooo

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an infinite sided polygon is always a circle

[jovial valve]

I think ik

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oh wow

that'd be real good

[jovial valve]

whats gonna be the radius

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exactly

[jovial valve]

if we continue chopping

whats the 1 point

that will always stay there

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also need to find area of p1

[jovial valve]

oo I know

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damn

[jovial valve]

that we can do later

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sure

[jovial valve]

what are the 3 points

that are always gonna stay inside

we chopping the edges right

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yep

[jovial valve]

I mean corners

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the midpoints of the sides

so the medians

[jovial valve]

yes

now we need radius

so we need distance ffrom centre to midpoint

remember something about height being divided into 1:2 parts

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?

we need to find the distance of any median from the centre right

[jovial valve]

yes

so in an equilateral triangle

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yes?

[jovial valve]

if we make a perpendicular bisector from 1 side

the perpendicular bisector will go through center and till midpoint right

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yep

like this

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yes

do you know about the ratio of top part and bottom part

of height

when divided from centre

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uh no

sorry

[jovial valve]

I am 99% sure it was 2:1

but imma derive it once to check

yes 1:2

[jovial valve]

lets derive it

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cool

[jovial valve]

you know trigonometry right ?

[river shoal]

yep

[jovial valve]

okie take the triangle BOD

sin 30 = 1/2, and angle in BOD is 30, take sin from there

OD/BO = 1/2

OD = OA

so OA = 2OB

[river shoal]

yep

[jovial valve]

now we have the ratios

we gotta find value of height

do we have side given ?

[jovial valve]

oo we know area

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correct

area is bh/2

so we can solve for h

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but we don't know b either

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we can get it

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yee

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with equilateral triangle formula

[jovial valve]

we gotta write 1 in terms of other

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it came to around 3.3

[jovial valve]

height ?

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one sec

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or side

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around 6.04

[jovial valve]

height ?

[jovial valve]

whats this

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yeah

height is 6.04

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each side of the triangle

[jovial valve]

hm that can't be right

height is bigger than sides ?

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wait no

i screwed up

[jovial valve]

if side is a
a^2 = h^2 + a^2/4

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height is 4.8

[jovial valve]

oo okie

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wait no

side is 4.8

[jovial valve]

thats side ?

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height is 4.16

[jovial valve]

yee figured

okie now 4.16

we gotta find distance from midpoint to centre

it should be 4.16/3 right ?

[river shoal]

radius is 4.16/3?

[jovial valve]

yee

[river shoal]

so that's it?

💀

[jovial valve]

yup

we got radius now we can get area easily

[river shoal]

so it's around 6.04cm^2

damn

you're crazy smart

which grade are you in

[jovial valve]

yup

[jovial valve]

12th

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ah nice

[jovial valve]

now for P1 area

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right

[jovial valve]

I think we can get that by drawing

[river shoal]

i used the law of cosines

[jovial valve]

Ooo did you get it ?

[river shoal]

lemme check one sec

[jovial valve]

was it around 6.666666667

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one sec

i got 1.6 💀

how did you get that

[jovial valve]

I might have been wrong tho

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how did you do that

side is around 4.8

[jovial valve]

I cut three corners

but sadly

[river shoal]

4.8/3 = 1.6

[jovial valve]

I cut it bad

lemme see how many divisions

wait I cut it right

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so i did 1.6^2+1.6^2-2(1.6)(1.6)(cos60)

under root

[jovial valve]

wait lemme show you

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won't cutting off 1/3 of each side make another equilateral triangle

[river shoal]

sure

[jovial valve]

its trisected 😋

and all the triangles have equal areas

hexagon left has 6 triangles tho, and our cut parts have 3

so same division as before

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there's 3 more inside right

[jovial valve]

yee

[river shoal]

like there's 6 tringles if you cut em off

alright cool

[jovial valve]

how

why cut 6

[river shoal]

if you cut the 3 edge triangles off

there's 6 left

[jovial valve]

ye

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ok

[jovial valve]

those 6 left will be P1

P2 will be traumatic

actually tho

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so the side of the hexagon will be 3.2

[jovial valve]

as I am pursuing gonna be a comp engineer

I can take

pi = e

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what

[jovial valve]

and area of P infinity approx = P1

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what

[jovial valve]

approximating 😋

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10 != 6

[jovial valve]

no thats p0

I mean P1

[river shoal]

i doubt it'll work for the solution

well yeah

[jovial valve]

6.6 = 6.0

[jovial valve]

it won't

[river shoal]

i got the side of the hexagon

now just gotta plug it into the formula

[jovial valve]

its just I am an engineering student so we love approximating

[jovial valve]

Ooo

[river shoal]

so am i 💀

[jovial valve]

Ooo

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but my major is physics lmao

[jovial valve]

approximate with me

[jovial valve]

uni ?

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i mean intended, i'm only in the 9th grade

[jovial valve]

ohh

it will be physics

mine will be comp sci

[river shoal]

i need a proper solution lol

isn't that possible

[jovial valve]

okie lets do that

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thanks so much

[jovial valve]

what was triangle's side

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big triangle or smaller ones?

big one is 4.8, smaller one is 3.2

[jovial valve]

4.8

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wait no

[jovial valve]

how tho

we are trisecting it right

so we have 4.8/3 left

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it's 1.6

[jovial valve]

1.6

yee

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mbmb

so now we can just find the area, multiply by 6

[jovial valve]

yup I was right 😋

[river shoal]

because these are equilateral triangles

[jovial valve]

multiply by 6 ?

[river shoal]

yeah

[jovial valve]

oh no that soln was totally different

forget that imma explain that later

[river shoal]

coz there's 6 triangles?

🧠

oh ok

[jovial valve]

oh you are finding area of triangles

[river shoal]

yep

[jovial valve]

I thought area of hexagon formula

[jovial valve]

you gotta find height too for that

too much work

[river shoal]

isn't it equilateral

[jovial valve]

oh ye

you can use the formula

still too much work tbh

when area of hexagon formula is this 🔥

[river shoal]

i have a calculator

[jovial valve]

Oooo

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lmao

so a = 1.6*2 = 3.2?

[jovial valve]

after we complete this imma explain 6 triangles easier method

[river shoal]

💀 wait what

[jovial valve]

square ?

[river shoal]

that is giving 26

[jovial valve]

side square is square

you forgot multiplying by $\frac{\sqrt{3}}{4}$

[river shoal]

2.56 gives 17

[iron stratus]

Akki#gtfoanemia#ViataGod

[river shoal]

i'm just plugging into formula

[jovial valve]

which formula

[river shoal]

on google

[jovial valve]

ohh

plug 1.6 in then

[river shoal]

6.65

[jovial valve]

very close to what I got

so back to my drawing

[river shoal]

yep

[jovial valve]

area of entire triangle is 10 right

and it got divided in 1:2 parts

3:6 1:2

[river shoal]

right

[jovial valve]

so if we divide 10 by 3, then multiply by 2

we have area of hexagon ?

[river shoal]

wait what

how

[jovial valve]

entire triangle is 10

we divide it in triangles that are in ratio 1:2

we need area of the 2

[river shoal]

💀 my brain is not braining

[jovial valve]

you understand the division ?

3:6 where we need 6

[river shoal]

no, that's what i don't get

[jovial valve]

3:6 is ratio of gone and kept

[jovial valve]

3 gone, 6 left

1 gone 2 left

simplified the ratio

[river shoal]

oh i got it

there's 9 triangles to begin with, 6 left

[jovial valve]

yee

[river shoal]

got it

[jovial valve]

9/6 is not fun ratio tho

cuz 3/2

1/2 >>>>

[river shoal]

🤷‍♂️

it works

[jovial valve]

yee

[river shoal]

just gotta multiply 10*6/9

[jovial valve]

yup

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and we have area of hexagon

now for p2

[jovial valve]

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will it be a polygon of 12 sides?

💀

[jovial valve]

I dislike P2 with all my heart

because I can't draw

its not equal

its not fair

area formula is

A = 3 × ( 2 + √3 ) × s^2

got it frm google

can't derive this, it will make me go crazy

[river shoal]

💀

[jovial valve]

lets just assume its gonna be 6 lol

its gonna be real close to 6

[jovial valve]

did you find side ?

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nope

[river shoal]

can't 🙏

@jovial valve you there?

[jovial valve]

yee

was using calculator

and its coming around 3 which is not possible

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how did you get the side

[jovial valve]

1.6/3 ?

what did we get for area of circle

around 6.004 right

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a/3 is the side of each side of the smaller triangles which make p1

[jovial valve]

yes

we gotta trisect it again right

[river shoal]

yeah

so it's a/9

so it's around 0.53

[jovial valve]

yes

which gives answer around 3

[river shoal]

now how many triangles are being used

[jovial valve]

which is not possible because then circle is wrong

[river shoal]

to make the p2 polygon

[jovial valve]

triangles won't be equal

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how many sides does it have

[jovial valve]

it only works for equilateral triangle

[river shoal]

rip

how many sides does p2 have

12?

[jovial valve]

wait lemme check

it probably has 12

yee

[river shoal]

p2 causes hate in my heart

[jovial valve]

but

P2 doesn't have equal sides

every alternate side is equal

[river shoal]

💀

[jovial valve]

guess this is why they didn't ask p3

who is asking this stuff to 9th graders

[river shoal]

lmao

[jovial valve]

man wants you guys to become no lifers

[river shoal]

ah well

i am

lmao

[jovial valve]

for now

[river shoal]

🤷‍♂️

[jovial valve]

we can probably find the other side tho

[river shoal]

other side?

oh there's 2 dimensions

one is 5.3, no one knows the other one

[jovial valve]

0.53 ☠️

[river shoal]

oh right mb

[jovial valve]

oooo we can do this

we know both sides of that triangle

we know its isoceles

we know the big angle

we can find small angles

[river shoal]

law of cosines?

[jovial valve]

then big side

yee

first find small angles

[river shoal]

wait what is the big angle

[jovial valve]

angle in hexagon

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120 degs

[jovial valve]

other 2 will be 30 then

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right

[jovial valve]

just gotta find the big side now

smaller sides are gonna be 0.53

[river shoal]

the equal sides are 0.53 right?

[jovial valve]

yee

[river shoal]

alr cool

why did we need the smaller angles

[jovial valve]

idk

[river shoal]

couldn't we have used law of cosines right away

[jovial valve]

well true

[river shoal]

it's 0.85

wait no

0.92

but please do check my work

[jovial valve]

☠️

[river shoal]

did i get it wrong 💀

[jovial valve]

I think I am gonna go with whatever you say

[river shoal]

oh well

it's 1 am

[jovial valve]

yes

0.92

[jovial valve]

it is

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good

so now we have the sides

[jovial valve]

how

we know only regular dodecagon formula

[river shoal]

i mean the sides of the triangle

[jovial valve]

there are no triangles this time

WAIT

YESSS

[river shoal]

?

[jovial valve]

great idea

[river shoal]

thanks lol

[jovial valve]

yes

take triangles

and subtract

no triangles inside

by 6 triangles outside

[river shoal]

🧠 not 🧠 ing

[jovial valve]

that we just chopped off

[jovial valve]

hexagon area

• 6 triangle area

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right

[jovial valve]

find area of the triangle

[river shoal]

heron's formula

[jovial valve]

or

find the height

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oof

[jovial valve]

you know all 3 angles

😋

[river shoal]

how many are there

[jovial valve]

6

all equal

[river shoal]

maybe there's smth wrong with me or i don't know what is up

but how the hell would i do that

[jovial valve]

okie remember this

we have 6 sides of hexagon where we cut those from right

soo

lets find area of 1

we know all of its sides and angles

[river shoal]

how

right

[jovial valve]

find height

[river shoal]

pain but alright

30-30-90 triangle?

wait

30-60-90

[jovial valve]

what

30-30-120 triangle

there is something wrong tho, its a little too big

[river shoal]

to find the height

we need 30-60-90

height is 0.266666

[jovial valve]

for that

we cut

yee

now using height

we get area of 0.12

which multiplied by 6 is 0.72

which can't be true

oo one min

[river shoal]

area is 0.07

[jovial valve]

what

what was base ?

[river shoal]

area of each triangle

0.53

[jovial valve]

oh

ohh

you got area of 2 sub triangles

[river shoal]

wdym

[jovial valve]

we are doing too much approximations

[river shoal]

fr

i will die if you tell me to restart

[jovial valve]

☠️

lets just

plug in other values

for last par

[river shoal]

what values

[jovial valve]

side of big triangle, side of hexagon, small side of dodecagon ☠️

we need to go into more decimals

[river shoal]

big triangle as in the one trisected from p0?

[jovial valve]

yes

[river shoal]

it's side is 1.601874276

[jovial valve]

wha

its side was around 4.8 right

which we divided by 3

for hexagon

[river shoal]

that was the side of the whole p0

divide by 3 to get this

[jovial valve]

we did everything correct

[river shoal]

i know

[jovial valve]

how is this not correct then

[river shoal]

why is answer not answering 🙏

[jovial valve]

how are we off by 0.12

[river shoal]

wait

[river shoal]

let's start again from here

measure of smaller side = 0.533333333333333333

[jovial valve]

I just checked all our calculations from there 😭

[river shoal]

wait

💀 the hell did we do wrong

[jovial valve]

I have no idea

we could say question is wrong

but

we are solving a general case

question can't be wrong

and circle radius can't be wrong either

[river shoal]

[jovial valve]

nothing can be wrong

but nothing is right

if I didn't know area of circle I would have even said its right

but I know

[river shoal]

💀

[jovial valve]

maybe

we both just need sleep

I am not even sleepy tho

its just

math isn't mathing

brain is braining

question is questioning

[river shoal]

exactly ugh

[jovial valve]

came

[jovial valve]

yee make it n=0 in start

he did a typo

[river shoal]

I see

[jagged fulcrum]

n=0 ze

[river shoal]

ze?

[jagged fulcrum]

se*

[river shoal]

ah

[cerulean lava]

💀

are you applying for PROMYS?

[river shoal]

wherever i ask for help everyone says this

what

is

it

smne tell me bruv

[cerulean lava]

where'd you find that problem?