Question

1. a window is shaped like a rectangle with a semicircle on each end. the rectangle is 16 in long and 10 in wide. each semicircle has a diameter of 10 inches. what is the total area of the window?

Explanation:

Step1: Calculate area of rectangle

The formula for the area of a rectangle is \( A_{rectangle} = length \times width \). Given length = 16 in and width = 10 in, so \( A_{rectangle} = 16 \times 10 = 160 \) square inches.

Step2: Calculate area of the two semicircles (equivalent to one circle)

The two semicircles on the ends make up a full circle. The diameter of each semicircle is 10 in, so the radius \( r = \frac{10}{2} = 5 \) in. The formula for the area of a circle is \( A_{circle} = \pi r^2 \). Substituting \( r = 5 \), we get \( A_{circle} = \pi \times 5^2 = 25\pi \approx 25 \times 3.14 = 78.5 \) square inches.

Step3: Calculate total area of the window

The total area of the window is the sum of the area of the rectangle and the area of the circle (from the two semicircles). So \( A_{total} = A_{rectangle} + A_{circle} = 160 + 78.5 = 238.5 \) square inches.

Answer:

The total area of the window is \( 160 + 25\pi \) (or approximately 238.5) square inches.