Calculus 1 Optimization

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 p  feet?

Answer 1

area of semi-circle is πr²/2

area of rectangle is (length x width)

 

width of rectangle = radius of semi-circle  l  = p

 

therefore, add both the areas  (πp²/2) + (lxw)