Question

a square whose sides are 12 inches long has been shaded and then overlaid with two quarter circles, each of which having a radius of 6 incches. What percent of the total area is shaded

Answer 1

71.8%

Explanation:

The shape described in question is a square overlaid with two quarter circles(a semi circle)

Area of the figure = Area of the square + area of the semi circle

Area of the figure =
`L^(2)+(\pi r^(2) )/(2)`

L = length of a side of the square = 12in

r is the radius of the semi circle = 6in

Area of the figure =
`12^(2) + (36\pi )/(2) }\\`

Area of the figure =
`144+18\pi` = 200.55in²

Since the shaded portion is a square;

percent of the total area is shaded = area of the square/total area * 100%

percent of the total area is shaded = 144/200.55* 100

percent of the total area is shaded= 71.8%