For a (filled-in) square of side length s we see |
P = Perimeter = 4⋅s, A = Area = s2, so P = 4⋅A1/2. |
For a (filled-in) circle of radius r we see |
P = Perimeter = 2⋅π⋅r, A = Area = π⋅r2, so P = 2⋅(√π)⋅A1/2. |
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Both the square and the circle have perimeters that are 1-dimensional, so these relations between area and perimeter can be expressed as |
p = k⋅Ad/2 |
where k is a constant that depends only on shape, not on size. |
Can you find the area-perimeter relationship for a rectangle? Here is the answer. |
Return to the area-perimeter relation.