Question

how is the area of a semicircle calculated if the radius is r?
a. ( a=\frac{1}{4}pi r^{2} )
b. ( a = pi r^{2} )
c. ( a=pi r )
d. ( a=\frac{1}{2}pi r^{2} )

Explanation:

Step1: Recall the area formula of a circle

The area formula of a circle is \(A_{circle}=\pi r^{2}\), where \(r\) is the radius.

Step2: Calculate the area of a semicircle

A semicircle is half of a circle. So, \(A_{semicircle}=\frac{1}{2}A_{circle}\).
Substitute \(A_{circle}=\pi r^{2}\) into the formula for the area of a semicircle: \(A_{semicircle}=\frac{1}{2}\times\pi r^{2}\).

Answer:

d. \(A = \frac{1}{2}\pi r^{2}\)