Question

the figure is made up of a rectangle and a semicircle.
note: not drawn to scale.
what is the area, in square feet, of the figure?

Explanation:

Step1: Calculate rectangle area

$\text{Area}_{\text{rectangle}} = 9 \times 6 = 54$

Step2: Find semicircle radius

$r = \frac{6}{2} = 3$

Step3: Calculate semicircle area

$\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (3)^2 = \frac{9}{2}\pi = 4.5\pi$

Step4: Sum both areas

$\text{Total Area} = 54 + 4.5\pi$

Answer:

$54 + 4.5\pi$ square feet (or approximately $68.14$ square feet if using $\pi \approx 3.14$)