This model of the backboard of a basketball goal is composed of a rectangle and a semicircle. Use the ruler provided to measure the dimensions of the model to the nearest half inch.
Which measurement is closest to the area of the model of the backboard in square inches?
18.56 in.2
31.12 in.2
12.28 in.2
23.56 in.2
To find the area of the backboard model, we first need to find the dimensions of the rectangle and the semicircle.
Rectangle:
Length = 18.5 in
Width = 12.5 in
Semicircle:
Radius = 6 in
Area of rectangle = Length x Width = 18.5 in x 12.5 in = 231.25 in²
Area of semicircle = 0.5 x π x (6 in)² = 18π in² ≈ 56.55 in²
Total area = 231.25 in² + 56.55 in² ≈ 287.8 in²
Therefore, the closest measurement to the area of the model of the backboard in square inches is 31.12 in².