Math CentralQuandaries & Queries


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?


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?


Scott wrote back

Yes that's it. Sorry I didn't explain it better.


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


x = √43,560 = 208.71 feet.

Hence the radius of the inscribed circle is 208.71/2 = 104.36 feet.

a square acre

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.


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