Question #61142

2 Answers
Nov 5, 2017

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

Nov 5, 2017

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