Question

find the area of the composite figure, which is a semicircle atop a rectangle. the figure is not drawn to scale.
write your answer as an exact number or round to the nearest hundredth.
draw
16 ft
14 ft

Explanation:

Step1: Calculate rectangle area

$A_{rectangle} = 14 \times 16 = 224$ square feet

Step2: Find semicircle radius

$r = \frac{14}{2} = 7$ feet

Step3: Calculate semicircle area

$A_{semicircle} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (7)^2 = \frac{49}{2}\pi = 24.5\pi$ square feet

Step4: Sum the two areas

$A_{total} = 224 + 24.5\pi$

Answer:

Exact value: $224 + 24.5\pi$ square feet
Rounded to nearest hundredth: $224 + 24.5\times3.1416 \approx 301.07$ square feet