The perimeter of the bigger octagon that is similar to the smaller one is: 238 units.
<h3>What is an Octagon?</h3>An octagon can be described as a polygon that has 8 sides and 8 angles.
What are Similar Octagons?
Octagons are referred to as similar to each other if they have the same angle measure but corresponding sides that are proportional to each other. That is, they have the same shape but different sizes.
How to Find the Perimeter of Similar Polygons?
Given the two octagons in the diagram are similar, and:
Perimeter of the smaller octagon = 34 units
A side of the smaller octagon = 4 units
Perimeter of the bigger octagon = ?
A corresponding side of the bigger octagon = 28 units
Therefore:
Perimeter of the smaller octagon/Perimeter of the bigger octagon = side of the smaller octagon/corresponding side of the bigger octagon
Plug in the values
34/Perimeter of the bigger octagon = 4/28
Perimeter of the bigger octagon = (28 × 34)/4
Perimeter of the bigger octagon = 238 units.
In summary, the perimeter of the bigger octagon is: 238 units.
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