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Largest area by shape

Largest area by shape

Circle always possess the largest area for the given perimeter of any two dimensional shape.

Lets consider the shape of circle, square, ellipse, octagon having the same perimeter. Let us consider perimeter to be 10.

This can be found by substituting in algebraic terms.

Area of the circle is pi.r2 where r = p/(2xpi) , r = 10 / (2 x 3.14) =10/(6.28) = 1.59

substituting in the equation pi.r2 = 3.14 x (1.59)2= 3.14 x 2.52 = 7.9

Area of the square is s2, s= p2/16 , = 102 /16 = 100 / 16 = 6.2

Area of the octagon is (2 + 2√2)s2, S = p2/64

So the area of an octagon is (2 + 2√2)p2/64

When substituting the values of perimeter, (2 + 2√2) 102/64 = 7.5

Area of the octagon is = 7.5

Thus the result clearly proves that circle will always have the largest area with any two dimensional shape having the same perimeter.

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