Question

Can someone explain how this is the answer to this question. (picture attached)

Answer 1

uhh...i can try

Answer 2

that is the question, i messed up on the notes and got confused lol

Answer 3

lol uhh..im kinda confused too


but i love your hand writing :)

Answer 4

@helpme1.2 can you help us

Answer 5

@heybhai can you help too if you dont mind

Answer 6

Give me 3 mins @GamerGirl.1

Answer 7

@iPwnBunnies can you help

all of these people are smart :) they can help us

Answer 8

ok

Answer 9

haha thank you :)

Answer 10

your welcome

Answer 11

Oh man, this might get confusing trying to explain it in typing.

Answer 12

it's all right as long as u label stuff like "step 1, step 2" etc

Answer 13

It looks like you have a good hold on math due to the stuff around the problem, I'll see if I can just write it in words.

Answer 14

its ok

Answer 15

Welp, the area of the circle is pi*r^2, we can start from there. A side of the triangle is the same length as the radius.

Answer 16

i feel like im in math class...

Answer 17

oh yeah it was an equilateral triangle

Answer 18

Ooo, do you know something I don't know?
The area of a sector of the circle, what is that?

Answer 19

Don't tell me, hold on.

Answer 20

Do you agree that the area of segment = area of sector - area of triangle?

Answer 21

hmm

Answer 22

i do agree

Answer 23

Good, so. The shaded region = area of the circle - area of the segment?

Answer 24

yes

Answer 25

Great. Therefore,
shaded region = area circle - (area of sector - area of triangle)

Answer 26

The thing is that I don't think I don't know theformula for the sector of a circle.
I remember arclength = radius*angle(radians)

Answer 27

ooooh i know how to find the sector, it's the triangle I'm confused about

Answer 28

the sector formula is arc degree/360 * pi(r^2)

Answer 29

i think

Answer 30

Break it up into two right triangles. Find the area of one of them and multiply by two.

Answer 31

This is like the ultimate Precalc problem.

Answer 32

so it should look like 60/360 x pi12^2
and, wouldn't that make the triangle a 30-60-90 triangle?

Answer 33

ahahah thats funny I'm only in regular geo

Answer 34

Yeah, the right triangle you created would be a 30-60-90 triangle. And I won't know the answer b/c I don't know the area of a sector lol.

Answer 35

hah @iPwnBunnies your smart :)

Answer 36

oh snap i think i got it actually

Answer 37

i was just watching.. and writing ...

Answer 38

Make sure you're using radians for theta, if you're using this formula for Area of a sector:
A(sector) = (1/2)*theta*r^2

Answer 39

i never learned theta yet, i was using a dif formula

Answer 40

Oh, sorry. Theta means the angle.

Answer 41

ooooh well the sector is 24pi

Answer 42

but now idk what comes after that

Answer 43

Alright, I'm just saying you might get the wrong answer if you're using the wrong units. Idk the formula you have.

Answer 44

Did you find the area of the "right triangle" yet?
I'll write out what we found so far.
Shaded region = area of circle - (area of sector - area of triangle)

Answer 45

no, i couldn't figure the triangle out

Answer 46

Shaded region = 144pi - 24pi - area of triangle

Answer 47

Alright, hold on.

Answer 48

oh wait is the area 36 (square root) 3