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It depends on the shape. If it is a rectangle, we know that two of the sides are the same as the sides opposite them, so the missing side is the difference between half of the perimeter and the known side. If the perimeter is p, the known side is sk, and the missing side is sm,

sm = p ÷ 2 - sk = 0.5p - sk

Since the area (a) is the product of the two sides,

a = sk x (0.5p - sk) = 0.5psk - sk2

For example, if we know that the perimeter is 14 cm and one side is 5 cm, the other side is

sm = 0.5p - sk = 0.5 x 14 cm - 5 cm = 7 cm - 5 cm = 2 cm

The area is the product of the two sides, both of which we now have.

a = 5 cm x 2 cm = 10 cm2

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Q: What is the area if you have one side and the perimeter?
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