A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 58.9 ft. give the area A of the window in square feet when the width is 12 ft. Give the answer to two decimal places.

Answer 1

let the radius of the semicircle be x
then the width of the rectangle is 2x
let the height of the rectangle be y

(1/2)(2π(x)) + 2x + 2y = 58.9
πx + 2x + 2y = 58.9
when y = 12,
x(π+2) + 24 = 58.9
x(π+2) = 34.9
x = 6.79

area of window = (1/2)π(6.79)^2 + 12(6.79) = .....
when x = 12
y = 58.9 - 24 - 12π = appr