A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 50.700 ft. give the area A of the window in square feet when the width is 8.800 ft. Give the answer to two decimal places.

Answer 1

If the rectangular part has width x and height y, then we have a perimeter

x+2y+πx/2 = 50.700
8.8+2y+8.8π/2 = 50.7
y = 14.039

So, the area is
A = xy + π/2 (x/2)^2
= 8.8*14.039 + π/2 * 4.4^2
= 153.954