Shedding the Light on a Norman Window

A window lets in light and fresh air. Adding a semicircle to the top of a rectangular window not only lets in more light, but adds a decorative touch. 

Part IV Taking the Shape of Geometric Word Problems 

Find the total area of each window. The rectangular part of each window is 24 square feet, so the main interest is in the respective areas of the semicircles on top. The window with a 4-foot base has a semicircle on top with a diameter of 4 feet — or a radius of 2 feet. The area of a circle is found with A = nr2. The semicircle has half the area of the full circle, so the area of this 

The areas of the two Norman windows in the preceding problem are different by almost 8 square feet — a fairly large difference. You may be surprised to know that the perimeters of these two windows aren t nearly so different. 

The Problem Which has the greater perimeter a Norman window with a 4-by-6-foot base or a Norman window with a 6-by-4-foot base  

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