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What are the relationship between the area and perimeter of a plane figure? For instance, what formula can I use to get the perimeter of a plane shape using the area. Lets assume that the dimension and shape of the plane figure is unknown.

There is no single relationship between area and perimeter for a 2-D figure.

For example, take a rectangle with 2 sides equal to x and the other 2 sides equal to y. Then the area is xy and the perimeter is 2x+2y = 2(x+y). Equating these gives xy = 2(x+y), which is only one equation to solve for 2 unknowns. Just knowing the area doesn't provide enough information to uniquely determine the perimeter, and vice versa.

Take for example a rectangle with equal sides (that is, a square) equal to 9. The perimeter is 4(9) = 36 and the area is 9^2 = 81. If the sides of the rectangle are 10 and 8, then the perimeter is 2(10)+2(8) = 36, as before, but the area is 8(10) = 80.

You need to know something about the shape of the figure to specify a connection between area and perimeter.

Randy

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