Question

find the area of the semicircle
18.
image of a semicircle with diameter 24 in.

Explanation:

Step1: Recall the formula for the area of a full circle

The area of a full circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Determine the radius of the semicircle

From the diagram, the diameter of the semicircle is 24 inches. The radius \( r \) is half of the diameter, so \( r=\frac{24}{2}=12 \) inches.

Step3: Calculate the area of the full circle

Substitute \( r = 12 \) into the formula for the area of a full circle: \( A=\pi\times(12)^2=\pi\times144 = 144\pi \) square inches.

Step4: Find the area of the semicircle

The area of a semicircle is half the area of the full circle. So, the area of the semicircle \( A_{semicircle}=\frac{1}{2}\times144\pi = 72\pi \) square inches. If we use \( \pi\approx3.14 \), then \( A_{semicircle}\approx72\times3.14 = 226.08 \) square inches.

Answer:

The area of the semicircle is \( 72\pi \) square inches (or approximately 226.08 square inches).