# Thread: Express Area as a function of x

1. ## Express Area as a function of x

Hello,

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.

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

2. Originally Posted by l flipboi l
Hello,

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.

$\displaystyle A=pi(x/2)^2+x(15-x)$
$\displaystyle \pi\left(\frac{x}{2}\right)^2$ is the area of a whole circle of radius $\displaystyle \frac{x}{2}$

3. 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".