A norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window 10 m, express the area A of the window as the function of width x of the window.

Answer 1

let the width of the rectangle be x m
let the base of the rectangle be 2y m, making the radius of the semicircle equal to y m
(my semicircle sits on the y )

2x + 2y + (1/2)(2πy) = 10
2x + 2y + πy = 10
y(2 + π) = 10 - 2x
y = (10-2x)/(2+π)

area = 2x(2y) + (1/2)πy^2
= 4xy + (1/2)πy^2
= 4x(10-2x)/(2+π) + (1/2)π(100 - 40x + 4x^2)/(4 + 4π + π^2)

clean it up if need be
Note: I considered the width to be the vertical side of the rectangle. If the intent was to call the base x m, make the necessary changes in the algebra. The steps would be the same.

Answer 2

It this circumference of a circle is 44cm. find its area