Question

composite area relay
1.) the diagram shows a spot on a basketball court called the \key\.
12 ft
19 ft
what is the area of the key? use 3.14 for π.
3.) eileen admires a beautiful stained-glass window in a museum. the window and its dimensions are shown in the diagram below.

Explanation:

Step1: Identify shapes and dimensions

The "key" is a rectangle plus a semicircle.

• Rectangle height: $12$ ft, rectangle length: $19 - \frac{12}{2} = 13$ ft
• Semicircle diameter: $12$ ft, so radius $r = \frac{12}{2} = 6$ ft

Step2: Calculate area of rectangle

Area of rectangle = length $\times$ height
$\text{Area}_{\text{rectangle}} = 13 \times 12 = 156$ sq ft

Step3: Calculate area of semicircle

Area of semicircle = $\frac{1}{2} \pi r^2$, use $\pi=3.14$
$\text{Area}_{\text{semicircle}} = \frac{1}{2} \times 3.14 \times 6^2 = \frac{1}{2} \times 3.14 \times 36 = 56.52$ sq ft

Step4: Sum the two areas

Total area = rectangle area + semicircle area
$\text{Total Area} = 156 + 56.52$

Answer:

212.52 square feet