Question

Lin is making a window covering for a window that has the shape of a half-circle on top of a square of side length 3 feet. How much fabric does she need, in square feet?

a. 14.13 sq. ft.
b. 14.14 sq. ft.
c. 15.00 sq. ft.
d. 15.12 sq. ft.

Answer 1

The fabric needed for the window covering is 12.525 square feet.

Step-by-step explanation:

To find the fabric needed for the window covering, we need to calculate the area of the half-circle and the square separately and then add them together.

The area of a half-circle is given by the formula A = 1/2 * π * r^2, where r is the radius. Since the diameter of the half-circle is equal to the side length of the square (3 feet), the radius is half of the diameter, which is 3/2 feet. Using this radius in the formula, we get A = 1/2 * 3.14 * (3/2)^2 = 3.525 square feet.

The area of the square is given by A = s^2, where s is the side length. Since the side length of the square is 3 feet, we have A = 3^2 = 9 square feet.

Adding these two areas together, we get the total fabric needed: 3.525 + 9 = 12.525 square feet.