Question

homework - area, perimeter, and circumference
find the area of the shape below.
(there is a semicircle with a diameter of 4 cm in the image)

Explanation:

Step1: Identify the radius

The diameter of the semicircle is 4 cm, so the radius \( r=\frac{4}{2}=2 \) cm.

Step2: Use the semicircle area formula

The formula for the area of a full circle is \( A = \pi r^2 \), so the area of a semicircle is \( \frac{1}{2}\pi r^2 \). Substitute \( r = 2 \) into the formula: \( \frac{1}{2}\times\pi\times2^2=\frac{1}{2}\times\pi\times4 = 2\pi \approx 6.28 \) \( cm^2 \).

Answer:

The area of the semicircular shape is approximately \( 6.28 \, cm^2 \) (or \( 2\pi \, cm^2 \)).