Question

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 31 feet, express the area A of the window as a function of the width x (across the base) of the window.

Answer 1

Let the height of the rectangle be h and the radius of the semicircle be r.

Area of rectangle = (2r)*h = 2rh
Area of semicircle = 1/2 pi r^2
A = 2rh + 1/2 pi r^2
but there are two variables, so we'll first try to eliminate one of them.

Note that perimeter = 2h + 2r + pi r = 31
so h = 31 - r - pi/2 r = 31 - (1 + pi/2)r

Substitute that into our equation for area to get:

A = 2r(31-(1+pi/2)r) + 1/2 pi r^2
= 62r - 2r^2 - 1/2 pi r^2

@Yondaime Study this and see what you think.

Solution written by @AwmsA

Answer 2

Question?