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 has side lengths equal to 16.35 in. Find the area of the second octagon. A. 461.60 in2 B. 882.9 in2 C. 717.06 in2 D. 642.66 in2

Question

11-08-2017
Mathematics

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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 has side lengths equal to 16.35 in. Find the area of the second octagon. A. 461.60 in2 B. 882.9 in2 C. 717.06 in2 D. 642.66 in2

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merlynthewhizz merlynthewhizz · Answer 1 · 2017-08-18T23:08:00+02:00

Both regular octagons are similar, so we can apply the concept of similar shape regarding the length of the side and the area.

If the scale factor of side is 'n' then the scale factor of the area is 'n²'

Octagon A's side length = 10.9
Octagon B's side length = 16.35

Scale factor of side length = 16.35 ÷ 10.9 = 1.5
Scale factor of area = 1.5² = 2.25

Area of octagon A = 392.4
Area of octagon B = 392.4 × 2.25 = 882.9 in²

Correct answer: B