SOLUTION: the norman window with the dimensions of a rectangle with a base of 6 feet is topped by a semicircle. if the area of the window is 68.2 square feet, find the height h to the neares

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Question 268829: the norman window with the dimensions of a rectangle with a base of 6 feet is topped by a semicircle. if the area of the window is 68.2 square feet, find the height h to the nearest tenth of a foot.
Found 2 solutions by mananth, jsmallt9:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
the norman window with the dimensions of a rectangle with a base of 6 feet is topped by a semicircle. if the area of the window is 68.2 square feet, find the height h to the nearest tenth of a foot.
the base is 6 feet.o the diameter of the semi circle will be 6 feet and radius =3 feet.
area = L*W
68.2 = 6*W
w=11.37
total height of the window will be 11.37 +3 feet 14.37 feet

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(NOTE: A solution provided by another tutor fails to include the semicircle in the area of the window.)

The area of the window = the area of the rectangle + the area of semicircle on top.
The area of the rectangle is length times width. The width is 6 and we'll let x = the length. So the area of the rectangle is 6x.

The area of a circle is pi%2Ar%5E2. The area of a semicircle would be half of this: %281%2F2%29pi%2Ar%5E2. Since the radius of this semicircle is 3, the area of this semicircle is %281%2F2%29pi%2A%283%29%5E2+=+%281%2F2%29pi%2A9+=+%289%2F2%29pi

So the total area of the window is 6x+%2B+%289%2F2%29pi. And we are told that this area is 68.2. So
68.2+=+6x+%2B+%289%2F2%29pi
Now we solve for x. Subtract %289%2F2%29pi from each side:
68.2+-+%289%2F2%29pi+=+6x
And divide both sides by 6:
%2868.2+-+%289%2F2%29pi%29%2F6+=+x
This is the exact answer. We need a decimal approximation so we will use our calculators:
%2868.2+-+14.1371669411540690%29%2F6+=+x
54.0628330588459310%2F6+=+x
9.0104721764743218+=+x
Rounded to the nearest tenth of a foot, x = 9.0. x is the height of the rectangle. To get the total height (which is what the problem is asking you to find, I think) you will add the height of the semicircle to this giving 12.0 as an answer.