Question

find the area of the figure below, composed of a rectangle and a semicircle. round to the nearest tenths place.
14
4
answer attempt 1 out of 2

Explanation:

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=l\times w\). Here, \(l = 14\) and \(w = 4\). So, \(A_{rectangle}=14\times4=56\).

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 semicircle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Substituting \(r = 2\), we get \(A_{semicircle}=\frac{1}{2}\times\pi\times(2)^{2}=\frac{1}{2}\times\pi\times4 = 2\pi\approx2\times3.14 = 6.28\).

Step3: Calculate the total area

The total area \(A=A_{rectangle}+A_{semicircle}\). So, \(A = 56+6.28=62.28\approx62.3\).

Answer:

\(62.3\)