A Norman Window is a window that has the shape of a

Last updated: 7/13/2022

A Norman Window is a window that has the shape of a semicircle on top of a rectangle. Let's say that we have a Norman window with height of the rectangle y feet tall and a semicircle with radius x feet. The contractor building the window knows that there is going to be exactly 14 feet of trim around the outside of the window (three sides of the rectangle plus the semicircle). Now would be a great time to draw a picture for this problem. Go ahead, I'll wait. (A) Recalling that the circumference of a circle is C = 2πr, write a formula for the amount of trim and solve your formula for y in terms of x. y(x) = (B) Now recalling that the area of a circle is A = 72, write a formula for the area of the Norman window in terms of x. You will need to replace any instance of y with your answer from part (A). A(x) =