SOLUTION: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 36.900 ft. give the area A of the window in square feet when the width is

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 36.900 ft. give the area A of the window in square feet when the width is      Log On

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Question 918319: A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 36.900 ft. give the area A of the window in square feet when the width is 7.500 ft. Give the answer to two decimal places.
I tried multiplying the 7.500 by 2 and subtracting the total from the 36.900. Then I divided that number by two and multiplied the result by 7.500. Can you help?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The window looks like this:

The red%28perimeter%29 is 3 sides of the rectangle (1 width and 2 lengths) plus the half circumference at the top.
If the width is 7.5 ft, that is also the diameter of the semicircle,
so the circumference would be 7.5pi and half a circumference is 7.5pi%2F2=3.75pi .
We have the bottom (the width) and the top (the half circumference), adding up to
7.5%2B3.75pi feet.
The rest of the perimeter is the 2 vertical sides, (2 lengths of the rectangle), so
2%2Alength%2B7.5%2B3.75pi=39.6
In approximate numbers,
2%2Alength%2B7.5%2B11.781=39.6
2%2Alength%2B19.281=39.6
2%2Alength=39.6-19.281
2%2Alength=17.619
length=17.619%2F2
length=8.8095 feet.

The area is the area of the rectangle part plus half of a circle.
8.8095%2A7.5%2B%281%2F2%29%2Api%2A3.75%5E2=66.071%2B22.089%28rounded%29=88.16 square feet (rounded to 2 decimal places).