Question

area of irregular shapes
score: 1/5 penalty: 0.25 off
question
find the area of the figure below, composed of a parallelogram and
one semicircle. rounded to the nearest tenths place
answer attempt 1 out of 2
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Explanation:

Step1: Calculate the area of the parallelogram

The formula for the area of a parallelogram is \(A = base\times height\). Here, the base \(b = 26\) and the height \(h=10\). So, \(A_{parallelogram}=26\times10 = 260\).

Step2: Calculate the radius of the semicircle

The diameter of the semicircle is equal to the side of the parallelogram which is \(16\). So, the radius \(r=\frac{16}{2}=8\).

Step3: Calculate the area of the semicircle

The formula for the area of a circle is \(A=\pi r^{2}\). For a semicircle, \(A_{semicircle}=\frac{1}{2}\pi r^{2}\). Substituting \(r = 8\), we get \(A_{semicircle}=\frac{1}{2}\times\pi\times8^{2}=\frac{1}{2}\times\pi\times64 = 32\pi\approx32\times3.14 = 100.5\).

Step4: Calculate the total area

The total area \(A=A_{parallelogram}+A_{semicircle}\). So, \(A = 260+100.5=340.5\).

Answer:

$340.5$