Question

find the area of the figure below, composed of a rectangle and a semicircle. round to the nearest tenths place. 16 4 answer attempt 1 out of 2 submit answer

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=l\times w\). Here, \(l = 16\) and \(w = 4\).
\(A_{rectangle}=16\times4=64\)

Step2: Calculate the area of the semicircle

The diameter of the semicircle \(d = 4\), so the radius \(r=\frac{d}{2}=\frac{4}{2}=2\). The formula for the area of a full - circle is \(A_{circle}=\pi r^{2}\), and for a semicircle \(A_{semicircle}=\frac{1}{2}\pi r^{2}\).
Substitute \(r = 2\) into the formula: \(A_{semicircle}=\frac{1}{2}\times\pi\times(2)^{2}=\frac{1}{2}\times\pi\times4 = 2\pi\approx2\times3.14 = 6.28\)

Step3: Calculate the total area

The total area \(A=A_{rectangle}+A_{semicircle}\)
\(A = 64+6.28=70.28\approx70.3\)

Answer:

\(70.3\)