Question

what is the area of this figure?
15 ft
3 ft
9 ft
5 ft
6 ft
3 ft
11 ft
if necessary, round your answer to the nearest hundredth.
square feet

Explanation:

Step1: Identify the figure's components

The figure consists of a quarter-circle and a rectilinear shape (polygon). First, find the radius of the quarter-circle: total vertical height = 3 + 5 + 3 = 11 ft, so radius $r = 11$ ft.

Step2: Calculate quarter-circle area

Area of quarter-circle: $\frac{1}{4} \pi r^2 = \frac{1}{4} \times \pi \times 11^2 = \frac{121\pi}{4} \approx 95.03$ sq ft.

Step3: Calculate rectilinear shape area

Break the polygon into 3 rectangles:

1. Top rectangle: $15 \times 3 = 45$ sq ft
2. Middle rectangle: $9 \times 5 = 45$ sq ft
3. Bottom rectangle: $11 \times 3 = 33$ sq ft

Total polygon area: $45 + 45 + 33 = 123$ sq ft.

Step4: Sum total area

Total area = quarter-circle area + polygon area $\approx 95.03 + 123 = 218.03$ sq ft.

Answer:

218.03