Question

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 24 ft, express the area A of the window as a function of the width x of the window.

I don't understand what this question is asking.

Answer 1

I think this is what the window looks like. The length of the 3 rectangle sides, plus the 'circumference' the semi circle equals 24.

x + 2y + \(\pi\) r = 24 (or x + 2y + \(\frac{1}{2}\tau\) r =24 for my tauist friends :) )

The total area is given by the area of the rectangle plus the area of the semicircle. The area of the rectangle is \(x \times y\), and the area of the semicircle is \(\frac{1}{2}\pi\) r\(^2\) (or \(\frac{1}{4}\tau\) r\(^2\)).