Question

find the area of the figure below, composed of a parallelogram and one semicircle. rounded to the nearest tenths place

Explanation:

Step1: Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A = base\times height\). Here, the base \(b = 14\) and the height \(h=8\). So, \(A_{parallelogram}=14\times8 = 112\).

Step2: Calculate the area of the semicircle

The formula for the area of a full - circle is \(A=\pi r^{2}\). For a semicircle, \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). The diameter of the semicircle is equal to the side of the parallelogram which is \(12\), so the radius \(r = \frac{12}{2}=6\). Then \(A_{semicircle}=\frac{1}{2}\times\pi\times6^{2}=\frac{1}{2}\times\pi\times36 = 18\pi\approx18\times3.14 = 56.52\).

Step3: Calculate the total area

The total area \(A = A_{parallelogram}+A_{semicircle}\). Substitute the values: \(A=112 + 56.52=168.52\approx168.5\).

Answer:

\(168.5\)