Question

A circle with a radius of 5 sits in a 11 X 11 rectangle. What is the area of the shaded region?

Answer 1

Hi :) I'm guessing the shaded region is the region inside the rectangle but outside the circle.

To solve this problem, you need to find the area of the rectangle and area of the circle. Then subtract the circle's area from the rectangle's.

Area of a rectangle: length × width
The problem already tells you the area of the rectangle, because it says it is an 11 × 11 rectangle.
(11)(11) = 121

Area of rectangle: 121 units²


Area of a circle: $\pi r^2$
Plug in 5 for the radius r.

$\pi 5^2$ = 78.5

Area of circle: 78.5 units²


Now subtract 78.5 from 121.
121 - 78.5 = 42.5

The area of the shaded region is 42.5 units².