Question

A 3cm x 2cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.

Answer 1

44.24cm² On khan academy

Answer 2

The area of the shaded region is
`44.24\ cm^(2)`

Explanation:

we know that

The area of the shaded region is equal to the area of the circle minus the area of rectangle

step 1

Find the area of circle

The area of the circle is equal to

`A=\pi r^(2)`

we have

`r=4\ cm`

substitute

`A=\pi (4)^(2)`

`A=16\pi\ cm^(2)`

step 2

Find the area of rectangle

The area of rectangle is equal to

`A=(3)(2)=6\ cm^(2)`

step 3

Find the difference

`16\pi\ cm^(2)-6\ cm^(2)`

assume

`\pi=3.14`

`16(3.14)\ cm^(2)-6\ cm^(2)=44.24\ cm^(2)`