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Whatever the ratio of perimeters of the similar figures, the areas will be in the ratios squared.

Examples:

* if the figures have perimeters in a ratio of 1:2, their areas will have a ratio of 1²:2² = 1:4.

* If the figures have perimeters in a ratio of 2:3, their areas will have a ratio of 2²:3² = 4:9.

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If the figures are similar, all linear measurements are proportional, while equivalent areas are proportional to the square of the area. For example, if you increase the length by a factor of 10, both the width and the perimeter will also increase by a factor of 10; while the area will increase by a factor of 10 squared (= 100).

Q: What is the relationship between perimeters and areas of similar figures?

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No, in general that is not true. For two similar figures it is true. But you can easily design two different figures that have the same perimeters and different areas, or the same area and different perimeters. For example, two rectangles with a different length-to-width ratio.

Similar figures are geometrical figures, which have the same shape but not the same size

it is definitely similar figures!

Their angles are the same.

Similar figures.

Related questions

The areas are different.

if you add up all the sides but in a smart way

They must be the same.

they are related when you can multiply or divide them together and get a whole number

Perimeter will scale by the same factor. Area of the new figure, however is the original figures area multiplied by the scale factor squared. .

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No, in general that is not true. For two similar figures it is true. But you can easily design two different figures that have the same perimeters and different areas, or the same area and different perimeters. For example, two rectangles with a different length-to-width ratio.

Their perimeters are in the same ratio.

similar figures have the same shape but not the same lengths, while congruent shapes are the same as eachother.

The relationship between them is similar to father and son.

Congruent figures are always similar. However, similar figures are only sometimes congruent.

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