Question

find the area of the figure below, composed of a rectangle and one semicircle, with another semicircle removed. round to the nearest tenths place.

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\). Here, the length \(l = 12\) and the width \(w=8\). So, \(A_{rectangle}=12\times8 = 96\).

Step2: Analyze the semicircles

The two semicircles (one added and one removed) have the same diameter \(d = 8\), so the radius \(r=\frac{d}{2}=4\). The area of a full - circle is \(A=\pi r^{2}\). The area of the added semicircle and the removed semicircle cancel each other out (\(A_{semicircle\ added}-A_{semicircle\ removed}=0\) since they have the same radius).

Answer:

\(96.0\)