Express Area as a function of x

**l flipboi l** · January 6th 2010, 05:27 PM

Hello,

Can someone please help me with this problem?

Problem: A Norman window has the shape of a rectangle surmounted by a semicircle. 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.

This is what I got.

$A=pi(x/2)^2+x(15-x)$

**skeeter** · January 6th 2010, 05:34 PM

Originally Posted by l flipboi l

Hello,

Can someone please help me with this problem?

Problem: A Norman window has the shape of a rectangle surmounted by a semicircle. 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.

This is what I got.

$A=pi(x/2)^2+x(15-x)$

$\pi\left(\frac{x}{2}\right)^2$ is the area of a whole circle of radius $\frac{x}{2}$

**Archie Meade** · January 6th 2010, 05:54 PM

Where did "h" go ?

You need to write the perimeter = 30,
using 3 straight side lengths + semicircle length = 30.

You express "h" in terms of x with this.

Then you write area using skeeter's correction,
and h is then eliminated by substituting your formula for "h".

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