Question

module assessment review
find the area of the composite figure in terms of π.
20 feet
8 feet
20 feet
56 + 8π square feet
48 + 2π square feet
60 + 4π square feet
160 + 8π square feet

Explanation:

Step1: Calculate area of rectangle

The area formula for a rectangle is $A = l\times w$. Here, $l = 20$ feet and $w=8$ feet. So, $A_{rectangle}=20\times8 = 160$ square - feet.

Step2: Calculate area of semi - circle

The diameter of the semi - circle is 8 feet, so the radius $r=\frac{8}{2}=4$ feet. The area formula for a full - circle is $A=\pi r^{2}$, and for a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Substituting $r = 4$ into the formula, we get $A_{semicircle}=\frac{1}{2}\pi\times4^{2}=\frac{1}{2}\pi\times16 = 8\pi$ square feet.

Step3: Calculate area of composite figure

The area of the composite figure $A = A_{rectangle}+A_{semicircle}$. So, $A=160 + 8\pi$ square feet.

Answer:

E. $160 + 8\pi$ square feet