Question

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

PLSS Solve Both Thanks

Answer 1

Part 1) The area of the shaded region is
`576\ cm^(2)`

Part 2) The area of the shaded region is
`A=(18+4.5\pi)\ cm^(2)`

Explanation:

Part 1) Figure N 1

I assume that the figure ABCD is a square

we know that

The area of the shaded region is equal to the area of the square ABCD minus the area of semicircle BC plus the area of semicircle AD

therefore

The area of the shaded region is equal to the area of the square ABCD

The area of the square is

`A=24^(2)=576\ cm^(2)`

Part 2) Figure N 2

I assume that the triangle ABC is a right isosceles triangle

so

AB=BC

AB ⊥ BC

The area of the shaded region is equal to the area of triangle plus the area of semicircle

A) Find the area of the triangle ABC

The area of triangle is

`A=(1)/(2)(AB)(BC)`

substitute

`A=(1)/(2)(6)(6)`

`A=18\ cm^(2)`

B) Find the area of semicircle

The area of semicircle is equal to

`A=(1)/(2)\pi r^(2)`

we have

`r=BC/2=6/2=3\ cm` -----> the radius is half the diameter

substitute

`A=(1)/(2)\pi (3)^(2)`

`A=4.5\pi\ cm^(2)`

therefore

The area of the figure is equal to

`A=(18+4.5\pi)\ cm^(2)`