Question

Question #61142

Answer 1

`8.58 sq. units`

Explanation:

The area of the square with the length `2sqrt10` is:
`(2sqrt10)^2 = 40`

The diameter of the inscribed circle is `2sqrt10`.
The area of the circle can be computed as:
`A=(pid^2)/4`
`A=(pi(2sqrt10)^2)/4`
`A=10pi=31.42`

Subtracting the area of the circle from the area of the square.
`40 -31.42`
`8.58 sq. units`

Answer 2

Given, that the side of the square is `s = 2sqrt10` ft, then the radius of the circle is `r = sqrt10" ft"`.

The area of the square is:

`A_"square" = s^2`

`A_"square" = (2sqrt10" ft")^2`

`A_"square" = 40" ft"^2`

The area of the circle is:

`A_"circle" = pir^2`

`A_"circle" = pi(sqrt10" ft")^2`

`A_"circle" = 10pi" ft"^2`

The area not covered is:

`A = A_"square" - A_"circle"`

`A = 40" ft"^2 - 10pi" ft"^2`