circular measure(or whatever it's called. circles and sector thing)

[odd shore]

Hot to find (ii).
Sorry for the bad hand writing and the poor lighting there's a power cut right now

[outer condor]

circular measure(or whatever it's called. circles and sector thing)

[elder snow]

Alright before we solve that problem, I want you to solve this problem (it has something that we are gonna use when solving your problem)

[elder snow]

Excellent job!!!

now let’s solve the problem you have sent

[odd shore]

Thanks

[elder snow]

Ok let’s start solving by drawing this line (or let’s say connecting those two points)

What do you think the angles green and red are? 🤔

[odd shore]

45° because it's a right angled triangle and since it's sides are radiuses they're equal making the angles equal

[elder snow]

Yes! Exactly

Now how can we find the radius of the circle with the center Q? (note that we can also call the circle with center Q as C(Q,R))

[odd shore]

We know the two sides(opposite and adjacent) are 5cm and it's a right angled triangle so we can use Pythagoras theorem to get side R

[elder snow]

Exactly! and so what would be the length of the radius?

[odd shore]

7.071067812cm
7.07cm

[elder snow]

Yep!

let’s just use 5sqrt(2) for now because it’s easier

Now let’s move on to the important part of the solution, areas 👻

Do you agree with the thing shown in the picture?

section A is the answer

section B is the whole semi-circle

section C is that weird looking part

[odd shore]

Yes

[elder snow]

Ok nice

I’m sure you can easily find the area of the semi-circle

but the other one (section C) is a little harder

so let’s focus on that part

[odd shore]

Yeah
Okay

[elder snow]

Ok now tell me whatever you think about the way of finding the area of this shape?

(If you don’t have any ideas, think about separating the shape into two parts)

[odd shore]

Finding the area of sector POQ seems easy enough but when it comes to POM I'm blank

[elder snow]

yes!! That’s exactly what we want to do

so POQ is easy for you which is nice

but what’s interesting about this problem

is that for finding the area of POM, we again have to do separating xD

[odd shore]

Oh okay

[elder snow]

take a look at this picture, can you guess what we wanna do to find the area of POM?

[odd shore]

Ohhh i think I see it
PQM is a sector so we find the area of that then theres a triangle(POQ) inside which we can also find the area of so we subtract the area of the triangle from the area of the sector to get the area of POM

[elder snow]

EXACTLYY!11! 🔥

Now try to find the area and tell me the value

(use square root and pi btw I don’t wanna use irrational stuff 💀)

I mean not for example 5.432 xD

ok yeah go on

[odd shore]

Okay so the area of the sector is
A = ⅛ pi × 49.9849 cm²
Triangle area = 12½ cm²
Area of POM = 6.2481pi - 12.5

I'm a bit confused on what you mean by square roots so sorry if I didn't I made a mistake in how I brought out the answer

[elder snow]

your answer is completely correct!

the reason I’m telling you to keep the length like 5sqrt(2)

is because when you wanna for example fine the area of the circle

It would be:

5sqrt(2) * 5sqrt(2) = 25 times 2 = 50

instead of 49.989

But still

It’s alright for now since you are allowed to use calculators!

[odd shore]

Oh I see

[odd shore]

Oh I know see how to find the area of the shaded region thank you so much you've helped alot

[elder snow]

You are welcome!

also I thank you for being here and actually thinking on the problem!

cya later mate 👋

[odd shore]

Np its easier when I'm walked through the problem rather than just given an answer

[elder snow]

Please don’t forget to close the forum 😅