Question

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 32 ft, express the area A of the window as a function of the width x of the window.

A(x) = ?

Answer 1

So, if x is the width, then, the area of the window will be given by the sum of the area of the rectangle and the semicircle, let's call z the heigth
\[A(x)=x*z+\frac{ \pi }{ 2 }( \frac{ x }{ 2 })^2\]
So we have to determinate "z"
The perimeter of the window is fiven by the sum of the perimeter of the semicircle and the rectangle without a side
\[32ft=P=\pi*\frac{ x }{ 2 }+2z+x\], now with that you can find z(x) and replace it on A(x)
cool?