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In general the larger the perimeter (of a flat shape) the greater the area. Given two congruent shapes the one with the larger perimeter has a greater area.

But two shapes that are not congruent (or almost so) do not follow this rule: for example a rectangle fifteen units long and one unit wide has an area of 15 square units and a perimeter of 32 units. While a square with edges four units has an area of sixteen square units (one more than the other rectangle) but a perimeter of only sixteen units (half that of the long thin rectangle).

So too with surface area and volume. Of two congruent 3 dimensional shapes, the one with the larger volume will also have a larger surface area.

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Q: How is area perimeter and volume related?
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What is the same of perimeter area and volume?

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