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

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 49 feet?

Answer 1

This is a combined shape problem. You will need to determine both the area of the semi-circle and the area of the rectangle. The area of the Norman window will be the sum of these two areas. First, you need to determine the circumference of the semicircle and the perimeter of the rectangle in terms of r, where r is the radius.