Norman window shape

Question

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 50 ft. give the area A of the window in square feet when the width is 10.1 ft. Give the answer to two decimal places.

Answer 1

Perimeter = 50

P = 50 = 2h + 10.1 + 10.1pi/2

h = 50-10.1 - 5.05pi = about 39.9 - 5.05(3.14) = 24.035

Area = A = 10.1h + pi(5.05)^2/2 = 10.1(24.035) + 3.142(25.503/2)= 242.75 + 80.12/2 = 242.75 + 40.6 = 283.35 ft^2

check the answer by simplifying and see if you're in the right range

let h =24, w=10, pi=3

A =hw + pi(w/2)^2/2 = 24(10) = 3(25)/2 = 240 + 75/2 = 240+ 37.5 = 277.5

A = 283.35 square feet looks about right