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 49 feet?

Answer 1

set da/dw = 0 when

w + 2h + πw/2 = 49

a = wh + π/8 w^2
= w(49 - (1+π/2)w)/2 + π/8 w^2