SOLUTION: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 8 ft, express the area A of the window as a function of the width x of th

Algebra ->  Surface-area -> SOLUTION: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 8 ft, express the area A of the window as a function of the width x of th      Log On


   

Question 1163706: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 8 ft, express the area A of the window as a function of the width x of the window.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The width of the window is x.

That is also the diameter of the semicircle.

The perimeter of the window is the width of the base (x), plus the circumference of the semicircle (half of pi times the diameter), plus twice the height of the rectangle.

The given perimeter is 8 feet.

x%2B%28pi%2F2%29x%2B2h+=+8 [1]

The area of the window is the area of the rectangle plus the area of the semicircle.

A+=+xh%2B%281%2F2%29%28pi%29%28x%2F2%29%5E2 [2]

Solve [1] to find h in terms of x; then substitute in [2] to get the area in terms of x.

A bit of ugly algebra to finish from there....

But that's where the "meat" of this problem is -- you would learn nothing from the problem if we finished the solution for you.