Question

Find the area of the shaded sections.

Answer 1

Do you know the formula for the area of a sector of a circle?

Answer 2

area of a circle => \(\bf \Large \pi r^2\)
area of a sector of a circle => \(\bf \Large \cfrac{\theta r^2 \pi }{360}\)

Answer 3

I believe it is\[\frac{ n }{ 360 }\times2\times(\frac{ 22 }{ 7 })\times(r)\]

Answer 4

\(\large {A_{sector} = \dfrac{n^o}{360^o} \pi r^2 }\)

Answer 5

yes that is correct

Answer 6

Good.
Now on to your problem.
You cna think of it as two sectors. Can you find the central angle of each one?

Answer 7

120 degrees. right?

Answer 8

I think I found the are of the triangle

Answer 9

I mean 8 times pi

Answer 10

nevermind. I thought the picture I posted said the angle of the shaded region was 120 degrees

Answer 11

i need to rework the problem

Answer 12

Each shaded sector has a central angle of 60 degrees.

\(\large {A_{sector} = \dfrac{n^o}{360^o} \pi r^2 }\)

The area of one shaded sector is:

\(\large {A_{sector} = \dfrac{60^o}{360^o} \pi 4^2 }\)

\(\large {A_{sector} = \dfrac{1}{6} \pi (16) }\)

\(\large {A_{sector} = \dfrac{16}{6} \pi }\)

\(\large {A_{sector} = \dfrac{8 \pi}{3}}\)

The area of both shaded sectors is

\(\large {A = 2 \times\dfrac{8 \pi}{3}}\)

\(\large {A = \dfrac{16 \pi}{3}}\)