SOLUTION: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 36 ft, express the area A of the window as a function of the width x of t

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Question 405566: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 36 ft, express the area A of the window as a function of the width x of the window.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A Norman window has the shape of a rectangle surmounted by a semicircle.
If the perimeter of the window is 36 ft, express the area A of the window as
a function of the width x of the window.
:
Let x = the width of the window and diameter of the semicircle
Let h = height of the rectangular portion of the window
:
Perimeter:
twice the height + the width + half the circumference = 36 ft
2h + x + .5x*pi = 36
2h + x + 1.57x = 36; convert pi to a decimal value * .5
2h + 2.57x = 36;
2h = 36 - 2.57x
h = %28%2836-2.57x%29%29%2F2
h = (18-1.285x)
:
Area = semicircle + rectangle
Radius = .5x
A = (.5*pi*(.5x)^2) + (x*h)
Convert pi to a decimal value times .5; Replace h with (18-1.285x
A = (1.57*.25x^2) + x(18-1.285x)
A = .3927x^2 - 1.285x^2 + 18x
A = -.8923x^2 + 18x