Question

The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal size. A shade for the window will extend 4 inches beyond the perimeter of the window, shown by the dashed line around the window. Each square in the window has an area of 100 in².

What is the area of the shade? Round your answer to the nearest whole number.

Answer 1

Area of the shade = Area of the entire structure - Area of the window.

Area of the entire structure = (48 x 44) + 1/2(pi x 24^2) = 2112 + 288pi
Area of the window = 40^2 + 1/2(pi x 20^2) = 1600 + 200pi

Area of shade = 2112 + 288pi - 1600 - 200pi = 512 + 88pi = 788 in^2