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| Math Central | Quandaries & Queries |
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Question from Scott, a student: I'm trying to find out the sq footage of the corners of an acre. If an acre is 43,560 sq and if I have this right the surface area of the circumference is 1040 ft. what is the combined square footage of the 4 corners? Or the percentage the original acre? |
Scott,
I don't understand what you are asking. Do you have a circle inside a square where the square has area an acre and you want the area in the corners outside the circle?
Harley
Scott wrote back
Yes that's it. Sorry I didn't explain it better.
Scott,
An acre is 43,560 square feet so if you have a square with area one acre and each side is x feet long then
x2 = 43,560
so
x = √43,560 = 208.71 feet.
Hence the radius of the inscribed circle is 208.71/2 = 104.36 feet.
What is the area of a circle with radius 104.36 feet? Subtract this from 43,560 square feet to find the area of the corner pieces.
Harley
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