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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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BlakeIf 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).
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Is it true that the greater the perimeter the greater the area?
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.
What is the definition for similar figures?
Similar figures are geometrical figures, which have the same shape but not the same size
Figures that have the same shape but not necessarily the same size?
it is definitely similar figures!
What do congruent and similar figures have in common?
Their angles are the same.
Having the same shape but not the same size?
Similar figures.
