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alexandr402 [8]
3 years ago
14

A regular octagon has side length 10.9 in. The perimeter of the octagon is 87.2 in and the area is 392.4 in2. A second octagon h

as side lengths equal to 16.35 in. Find the area of the second octagon.
Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
3 0

To solve this problem, let us first calculate for the Perimeter of the other octagon. The formula for Perimeter is:

Perimeter = n * l

Where n is the number of sides (8) and l is the length of one side. Let us say that first octagon is 1 and the second octagon is 2 so that:

Perimeter 2 = 8 * 16.35 in = 130.8 inch

We know that Area is directly proportional to the square of Perimeter for a regular polygon:

Area = k * Perimeter^2

Where k is the constant of proportionality. Therefore we can equate 1 and 2 since k is constant:

Area 1 / Perimeter 1^2 = Area 2 / Perimeter 2^2

Substituting the known values:

392.4 inches^2 / (87.2 inch)^2 = Area 2 / (130.8 inch)^2

Area 2 = 882.9 inches^2

 

<span>Therefore the area of the larger octagon is about 882.9 square inches.</span>

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