Question

1. mjhs is refinishing the basketball court and decided to paint everything shown below blue. how many square feet will be painted blue?

(there is a diagram of a rectangle with length 15 ft and height 10 ft, attached to a semicircle on one of the 10 ft sides. handwritten notes: a = bn (likely a = bh for rectangle area) and a = πr²/2 for semicircle area.)

Explanation:

Step1: Calculate area of rectangle

The rectangle has length \( 15 \) ft and width \( 10 \) ft. Area of rectangle is \( A_{rect} = length \times width \).
\( A_{rect} = 15 \times 10 = 150 \) square feet.

Step2: Calculate radius of semicircle

The diameter of the semicircle is equal to the width of the rectangle, \( 10 \) ft. So radius \( r = \frac{10}{2} = 5 \) ft.

Step3: Calculate area of semicircle

Area of a full circle is \( \pi r^2 \), so semicircle area \( A_{semicircle} = \frac{1}{2} \pi r^2 \).
Substitute \( r = 5 \): \( A_{semicircle} = \frac{1}{2} \pi (5)^2 = \frac{25\pi}{2} \approx 39.27 \) square feet.

Step4: Total area to paint

Add area of rectangle and semicircle: \( A_{total} = A_{rect} + A_{semicircle} \).
\( A_{total} = 150 + \frac{25\pi}{2} \approx 150 + 39.27 = 189.27 \) square feet (or keep it as \( 150 + \frac{25\pi}{2} \) for exact form).

Answer:

Approximately \( 189.27 \) square feet (or \( 150 + \frac{25\pi}{2} \) square feet)