Thread: Semi-Circle Rectangle Area, perimeter
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Old October 29th, 2009, 12:31 AM
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earboth earboth is offline
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Quote:
Originally Posted by goliath View Post
A window is in the shape of a semi-circle on top of a rectangle. The height of the rectangle is twice its width.

a) Give an expression for A, the area of the window, in terms of w, its width.
b) Give an expression for P, the perimeter of the window, in terms of w, its width.
c) Give an expression for A, in terms of P only.
I'll show you how you can do a):

The area of a rectangle is calculated by A_{rect}=length \cdot width

The area of a semi-circle is calcvulated by A_{sem-circ}=\frac12 \cdot \pi \cdot (radius)^2

... and now it's your turn.

With your question you know:
length = 2 \cdot width
radius = \frac12 \cdot width

Therefore the area of the window is:

A = 2 \cdot width \cdot width + \frac12 \cdot \pi \cdot \left(\frac12 width\right)^2 = (width)^2 \left(2 + \frac18 \pi\right)
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