Question

In the design shown below, four semicircles are attached to a square whose area is 36 square centimeters. Which of the following is closest to the total area of the shaded semicircles, measured in square centimeters?

Answer 1

56.549 cm (choice 1)

Explanation:

If the area of the square if 36 cm, then each side is 6 cm.

That means the diameter for each semi circle is also 6 cm.

Formula for a semi circle is 1/2(πr²)

We need the radius, which is half the diameter. So the radius is 6÷2= 3

Now plug in to the formula.

A= 1/2(π3²)

A= 14.137 (nearest hundredths)

Now multiply that by 4, because there are 4 semi circles

4(14.137)= 56.549 cm (nearest hundredths)