High School

An octagon has a side length of 10.9 in. The perimeter of the octagon is 87.2 in, and the area is 392.4 in². A second octagon has corresponding side lengths equal to 21.8 in. Find the area of the second octagon. Round to the nearest hundredth.

A. 98.1 in²
B. 1569.6 in²
C. 784.8 in²
D. 196.2 in²

Answer :

If the figures/solids are similar, the ratio of the areas is equal to the square of the ratio of the corresponding sides. Let x be the area of the second figure. The equation that would best allow us to answer this item is,
(394.2 in² / x in²) = (10.9 / 21.8)²
The value of x from the equation is 1576.8 in².

Thus, the nearest answer is the second choice.

Answer:

1569.6 in2

Step-by-step explanation:

(392.4 in² / x in²) = (10.9 / 21.8)²

The value of x from the equation is 1569.6 in2

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