Question

Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answer 1

`40\pi \ m^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

In this problem we have

`r=10\ m`

Substitute and find the area

`A=\pi (10)^(2)=100 \pi\ m^(2)`

Remember that

`360\°` subtends the area of complete circle

so

by proportion

Find the area of the shaded regions

The central angle of the shaded regions is equal to
`2*72\°=144\°`

`(100\pi )/(360) (m^(2))/(degrees) =(x )/(144) (m^(2))/(degrees) \\ \\x=144*100\pi /360\\ \\ x=40\pi \ m^(2)`