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

Answer:

71.8%

Step-by-step 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 = $L^{2}+\frac{\pi r^{2} }{2}$

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

r is the radius of the semi circle = 6in

Area of the figure = $12^{2} + \frac{36\pi }{2} }$

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%