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Why are area and perimeter not dependent on one another?

Updated: 9/17/2019
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7y ago

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That's because you can easily have two different shapes with the SAME perimeter, and DIFFERENT areas, or vice versa. Here is an example:* A 2x2 rectangle has an area of 4, and a perimeter of 8.

* A 1x3 rectangle has an area of 3, and a perimeter of 8.

* A 0x4 rectangle has an area of 0, and a perimeter of 8. (If you don't like this rectangle, you can make one that is arbitrarily close, i.e., a very small width.)

Note that for two SIMILAR figures, any linear measurements are proportional to the scale size, and any area measure is proportional to the square of the scale size - that will make the area proportional to the perimeter, but only for two similar shapes, e.g., two rectangles with the same length-to-width ratio.

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7y ago
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7y ago

For regular polygons , circles, and some other shapes they are dependent. But in general, the two measure different characteristics which results in the absence of dependence.

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Q: Why are area and perimeter not dependent on one another?
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They vary from one pool to another.


Can a rectangle have a greater perimeter than another one but have a greater area too?

yes it can; a rectangle 5 by 2 has perimeter 14 and area 10 for example; a rectangle 10 by 2 has perimeter 24 and area 20, both greater.


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Is perimeter larger than the area of square?

Perimeter is length or distance (inches, feet, meters). Area is square units (length2 : square inches, square feet, square meters), so to say that one is larger than another is not relevant. If it's a 1 by 1, then the perimeter is 4 and the area is 1. But if the square is 5 by 5, then it has a perimeter of 20 and an area of 25. It depends, good luck.


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