Expressing the area as a function (hard!)?

Question

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window.

Answer 1

width of window = x

thus height of window = (15 - x)

radius of semicircle = (x/2)

.. . .

area

rectangle: x(15-x)

semicircle: π(x/2)^2

thus

A = 15x - x^2 - (π/4) x^2