How do you find the the area of the rectangle if perimeter is given?

Answer 1

To find the area of a rectangle, when you only know the perimeter, you can just just break the sides down into two pairs of lengths. For example; if the known perimeter is 100, you can call the two short sides, we'll call those the width, 10 (x2=20) and the two long sides, we'll call those length, 40 (x2=80) 20+80=100... Now you know all the lengths of the sides, so the area formula is L x W = area or 10 x 40 = 400. Any rectangle with a perimeter of 100 will have an area of 400, no matter what the lengths are and the process works for any rectangle, you just have to break the perimeter length down into two pairs of lengths.

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That starts off right but is NOT the full method.

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You need to know the ratio between its length and breadth. Then apply that ratio to half of the perimeter to find the length and breadth.

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Try it:

L = 4, B= 6 so P = 20 but Area = 4 X 6 = 24 square units.

L = 2, B = 8 so P = 20 again BUT Area now = 2 X 8 = 16 sq. units.

For any given rectangle perimeter, there is an infinite number of possible areas.

For a quadrilateral, Perimeter-only works only for the Square, for which A = [P/4]^2 = [(P^2)/16]