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Strictly speaking an area cannot equal a perimeter because an area is a two dimensional concept while a perimeter is one dimensional. A shape can have the same number for its perimeter and its diameter but then thanks to the dimensionality of these measures, this is totally dependant on the units of measurement used.

For example a 4m * 4m square has an area of 16 m2 and a perimeter of 16 m. So far so good.

But the same shape could be describes as a 400cm * 400 cm square. Now area = 160000 cm2 while perimeter = 1600 cm.

Or, 13.1234 ft*13.1234 ft giving an area of 172.2226 square ft and a perimeter of 52.4934 ft.

So, through appropriate choice of the unit of measurement, the area and perimeter of any shape can be made numerically equal.

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Q: When is area equal to perimeter?
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