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A Norman window has the shape of a rectangle surmounted by a semicircle, as shown in the figure. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window.
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
The given figure consists of a semicircle and a rectangle in which the diameter of a semicircle is equal to the width of a window. Let's label further the figure above as follows
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| Photo by Math Principles in Everyday Life |
If the perimeter of a window is given in the problem, then the working equation is
