Question

find the area of the figure below, composed of a rectangle and a semicircle. the radius of the circle is shown. round to the nearest tenths place. 11 5

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=l\times w\). The length \(l = 11\) and the width \(w=2\times5 = 10\) (since the diameter of the semicircle is the width of the rectangle). So \(A_{rectangle}=11\times10=110\).

Step2: Calculate the area of the semicircle

The formula for the area of a full - circle is \(A_{circle}=\pi r^{2}\), and for a semicircle \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Given \(r = 5\), then \(A_{semicircle}=\frac{1}{2}\times\pi\times5^{2}=\frac{25\pi}{2}\approx\frac{25\times3.14}{2}=39.25\)

Step3: Calculate the total area

The total area \(A = A_{rectangle}+A_{semicircle}\). So \(A=110 + 39.25=149.25\approx149.3\)

Answer:

\(149.3\)