Question

Find, to the nearest tenth, the area of the region that is inside the square and outside the circle. The diameter of the circle is 14 in

Answer 1

Assuming you mean that the circle touches the sides of the square, the area of the square would be 14 x 14 = 196 sq in

The area of the circle inside of the square is π (7)² = 153.9

Therefore 196 - 153.9 = 42.1

Answer 2

Option
`42.1\ in^(2)`

Explanation:

we know that

The area of the region that is inside the square and outside the circle is equal to the area of the square minus the area of the circle

see the attached figure to better understand the problem

Step 1

Find the area of the square

Remember that

The area of the square is

`A=b^(2)`

where

b is the length side of the square

we have

`b=14\ in`

substitute

`A=14^(2)=196\ in^(2)`

Step 2

Find the area of the circle

Remember that

The area of the circle is equal to

`A=\pi r^(2)`

we have

`r=14/2=7\ in`

substitute

`A=\pi(7^(2))=153.9\ in^(2)`

Step 3

Find the area of the region

`196\ in^(2)-153.9\ in^(2)=42.1\ in^(2)`