Question

The length around the outside of semicircle O from point L through point M to point N is 14 centimeters. The perimeter of semicircle O is about 22.92 centimeters. What is the approximate area of semicircle O? Use 3.14 for . A. 41.83 square centimeters B. 83.67 square centimeters C. 62.46 square centimeters D. 31.23 square centimeters Reset

Answer 1

The area would be 83.67 cm.

A semicircle is half of a circle.  The perimeter of the semicircle would be half of the perimeter (circumference) of the entire circle.  The formula for circumference is:

C=πd

Using our information, we have  

22.92 = 0.5(3.14)d
22.92 = 1.57d

Divide both sides by 1.57:

22.92/1.57 = 1.57d/1.57
14.6≈d

Since the diameter is 14.6, the radius is 14.6/2 = 7.3.

We use the radius for the area of the semicircle:

A=0.5πr²
=0.5(3.14)(7.3)²
=83.67