Possible Norman Window

Question

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 40 feet?

Answer 1

Draw and label a diagram

w represents the width of the rectangle/semi-circle

h represents the height of the rectangle

2h = 40 - (wπ/2) - w

h = 20 - (wπ/4) - (w/2)

A = hw + (0.5)(π)(w²/4)

Substitute for h, determine first derivative, solve for 0.