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 22 feet?

This is an optimization question and maybe my online math program isn't taking my answer but I cannot get it right

Answer 1

Perimeter (circumference) of a circle is (pi)(d). d = diameter.
But we are dealing with a semi circle, so perimeter of a semi circle is (1/2)(pi)(d)
If you draw the window and call the rectangle's tall sides 'h', the bottom of the window is 'd', the perimeter of the top (semi circle) is (pi)(d) / 2. Area is (h)(d) for the rectangular part and (1/2) (pi) r^2 for the semicircle. we know that r = d/2.