function area ?

Question

A window has the shape of a rectangle with a semicircle on top. If the perimeter of the window is 28 feet express the area A of the window as a function of the width x of the window.

In case it is not clear, the shape of the window is like this:
http://www.ubicomp.lancs.ac.uk/~molyneau/gallery/albums/Lancaster/window.sized.jpg

Answer 1

Well Roger, you should first understand that the semicircular arc being mounted on the window, its diameter would be equal to the width of the rectangle (going by the general shape of the windows as you have shown).
You also might have understood that the area of the window is the sum total of the areas of the rectangular part and the semicircular part mounted over it.
Now let the length of the window be 'L. Width being given as another variable 'X', the perimeter (sum total of the length of each side) can be written as 2(X+L)=28, which is provided in the problem statement. From this, you get L=(14-X). Area of the rectangle is XL which by using the relation, becomes X(14-X).
As mentioned earlier, diameter of the semicircle mounted on the window is equal to the width 'X'. Hence, area of this semicirle becomes [3.14*(X)^2]/8. Hence the total area of the window in terms 'X' is:
A={X*(14-X)+[3.14*(X)^2]/8}. You can also take the common terms outside and rewrite the expression as:
A=(X)*{(14-X)+3.14*(X)/8}

Answer 2

Well, the width of the window does not have an effect on the problem, so I don't see how to answer it, but the area of the circle can be found by going

((pie)*(diameter)) / 2

(3.14*28) / 2

87.92 / 2

43.96 ft. is the area of the circle.

The area of the rectangle can be found by going x * 28.


hope this helps.