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Nina [5.8K]
3 years ago
15

The sides of two regular octagons are 3 in. And 6 in. respectively. Find the ratio of their perimeters and their areas

Mathematics
1 answer:
photoshop1234 [79]3 years ago
6 0

The ratio of their perimeters is \frac{1}{2} and the ratio of their areas is \frac{1}{4}

Step-by-step explanation:

A regular n-side polygon has

  • n equal sides
  • n equal angles
  • The measure of each interior angle = \frac{(n-2).180}{n}
  • 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>

<em />

∵ 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 = \frac{3}{6}

- Divide the two terms of the ratio by 3 to simplify it

∴ The constant ratio between their sides = \frac{1}{2}

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 = \frac{1}{2}

∵ The ratio between their perimeters = the constant ratio between

   their sides

∴ The ratio between their perimeters = \frac{1}{2}

∵ The ratio between their areas = (constant ratio)²

∴ The ratio between their areas = (\frac{1}{2})^{2}=\frac{1}{4}

The ratio of their perimeters is \frac{1}{2} and the ratio of their areas is \frac{1}{4}

Learn more:

You can learn more about the polygons in brainly.com/question/3779181

#LearnwithBrainly

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