The ratio of their perimeters is and the ratio of their areas is
Step-by-step explanation:
A regular n-side polygon has
- n equal sides
- n equal angles
- The measure of each interior angle =
- Its perimeter = n × a, where a is the length of its side
<em>V.I.Note: all regular polygons have same number of sides are similar, because their interior angles are equal in measures and their sides are proportion</em>
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∵ There are to regular octagons
- Regular octagon has 8 equal sides and 8 equal angles
∴ The two octagon are similar
∵ Their sides are 3 inches and 6 inches
∴ The constant ratio between their sides =
- Divide the two terms of the ratio by 3 to simplify it
∴ The constant ratio between their sides =
In similar figures <em>the ratio between their perimeters is equal to the constant ratio between their sides</em>, and <em>the ratio between their areas is equal to square the constant ratio between their sides</em>
∵ The two octagons are similar
∵ The constant ratio between their sides =
∵ The ratio between their perimeters = the constant ratio between
their sides
∴ The ratio between their perimeters =
∵ The ratio between their areas = (constant ratio)²
∴ The ratio between their areas =
The ratio of their perimeters is and the ratio of their areas is
Learn more:
You can learn more about the polygons in brainly.com/question/3779181
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