The window in the figure above consists of a rectangle and a semicircle…
We are given a semicircle with a diameter of 4 ft., which also represents the width of the rectangle. We are also given that height of the window is 10 ft., which is the combined length of the radius of the semicircle and the length of the rectangle. To determine the length of the rectangle, we can subtract the radius of the semicircle, which is 2 ft., from the total length of 10 ft., so we have:
10 – 2 = 8 ft.
Now we can calculate the area for the semicircle and the rectangle.
Area of semicircle = (1/2)π(2^2) = 2π
Area of rectangle = 8 x 4 = 32
Thus, the total area is 32 + 2π.