Question

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 27 feet, express the area A of the window as a function of the width x (across the base) of the window.

Answer 1

do you have a diagram ?

Answer 2

No, the question didn't have one...I can Google one if you'd like. It's all over the internet, this problem, really, but no solution seems correct, or I don't understand it.

Answer 3

I think it will look like a rectangle except the top of the rectangle will be a semi-circle instead of a straight line.

So the perimeter will be: x + 2H + pi * (x/2) = 27 feet ---- (1)

Area A = Hx + 1/2 * pi * (x/2)^2 ----- (2)

Find H from (1) and put it in (2) and simplify.

Answer 4

is it like this, ranga ?

Answer 5

Yes, I believe so.

Answer 6

oh ok, that make sense now :)
then your equation is right ...

Answer 7

Thank you very much! :)

Answer 8

You are welcome.