Question

What is the area of the shaded region in the given circle in terms of pi?
**Picture coming**

Answer 1

Do you know how to find the area of the entire circle

Answer 2

no

Answer 3

multiply all the sides 2 find the area

Answer 4

\[Area = π × r2 ^{2}\]

Answer 5

sides? its a circle

Answer 6

oh

Answer 7

LOL

Answer 8

i feel stupid

Answer 9

its all good :) hahaha so exactly how would i solve it?

Answer 10

well first you gotta find the hypotenuse of the triangle

Answer 11

this question is tossing my brain around like a rag doll

Answer 12

ha im sorry, so how would i find the hypotenuse?

Answer 13

find the area of the sector... subtract the area of the triangle...

sector angle = \[A = \frac{1}{6} \pi \times 6^2\]

area of the triangle
\[A = \frac{1}{2}\times 6 \times 6 \times \sin(60)\]

the the unshaded area is

Unshaed = Area of the sector - area of the triangle

so the total shaded area = area of the circle - unshaded

Answer 14

I think you should find the area of an equilateral triangle with side length of 6

Answer 15

I am really confused

Answer 16

ok... so the 1st task is to fins the unshaded area... does that make sense..?

Answer 17

yes

Answer 18

area of triangle is 15.58845727

Answer 19

ok... so the sector angle is 60 degrees so you are looking at a sector that is 60/360

or 1/6 of the circle...

so the area of the sector is

\[A = \frac{1}{6} \times 6^2 \times \pi\]

so the sector area

\[A = 6\pi\]

does that make sense...?

Answer 20

\[(30\Pi +9\sqrt{3}) m ^{2}, (24\Pi +9\sqrt{3}) m ^{2}, (30\Pi +18\sqrt{3}) m ^{2}, (24\Pi +18\sqrt{3}) m ^{2}\]

Answer 21

these are the answers

Answer 22

ok... lets forget the answers for a while...

now the area of the triangle.... its isosceles... 2 sides of 6 and a subtended angle of 60

so using trig

\[A = \frac{1}{2}\times a \times b \times \sin(C)\]

you can calculate this... a = 6, b = 6 and C = 60

evaluate it and post the answer...

Answer 23

leave the answer as an exact value...

Answer 24

15.5884572681

Answer 25

well as an exact value the triangle is

\[A = 9\sqrt{3}\]

so the unshaded Area = Area of the sector - area of the triangle

\[Unshaded = 6\pi - 9\sqrt{3}\]

now to find the area of the shaded section

Area of the circle is

\[A = \pi \times 6^2\]

shaded area = area of the circle - unshaded area...

I'll let you do the calculation

Answer 26

so the shaded area is

\[36\pi - (6\pi - 9\sqrt{3})\]

Answer 27

just simplify it

Answer 28

would the answer be A?

Answer 29

it would...