Area-Perimeter Relation: Euclidean Objects

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.

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.