Question

the figure below consists of a semi - circle and a rectangle. what is the area, in square feet, of the figure? (a) $50 + 2.5pi$ (b) $50 + 10pi$ (c) $50 + 12.5pi$ (d) $50 + 25pi$

Explanation:

Step1: Calculate rectangle area

The area formula for a rectangle is $A = l\times w$. Here, $l = 10$ ft and $w = 5$ ft. So, $A_{rectangle}=10\times5 = 50$ square - feet.

Step2: Calculate semi - circle area

The diameter of the semi - circle is equal to the length of the rectangle, so $d = 10$ ft, and the radius $r=\frac{d}{2}=\frac{10}{2}=5$ ft. The area formula for a full - circle is $A=\pi r^{2}$, and for a semi - circle is $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Substituting $r = 5$ ft, we get $A_{semicircle}=\frac{1}{2}\pi\times5^{2}=\frac{25\pi}{2}=12.5\pi$ square - feet.

Step3: Calculate total area

The total area of the figure $A = A_{rectangle}+A_{semicircle}=50 + 12.5\pi$ square - feet.

Answer:

C. $50 + 12.5\pi$