A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below....

Question:

A Norman window has the shape of a rectangle surmounted by a semicircle as in the figure below. If the perimeter of the window is 37 ft, express the area, A, as a function of the width, x, of the window.

Norman Window:

Note that the perimeter is the sum of the sides of the figure and for the norman window its perimeter formula is {eq}\displaystyle P=w+2l+\pi r {/eq} where {eq}w,l,r {/eq} are the width and length of the rectangular part of the widow and {eq}r {/eq} is the radius of the surmounted semicircle. The total area of the window is the sum of the area of rectangle and the area of semicircle.

Answer and Explanation:

Below is the figure,

Figure

Note that the radius of semicircle is one-half of the width of the rectangle. The perimieter is,

{eq}\displaystyle...

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