Question

the figures below are similar. the labeled sides are corresponding.
4 in.
2 in.
what is the ratio of the area of the smaller pentagon to the area of the larger pentagon?
write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3)

Explanation:

Step1: Recall the ratio of areas of similar figures

For similar figures, if the ratio of their corresponding side lengths is \(a:b\), the ratio of their areas is \(a^{2}:b^{2}\). Here, the ratio of the side lengths of the smaller pentagon to the larger pentagon is \(3:6 = 1:2\).

Step2: Calculate the ratio of the areas

Using the formula \(A_{1}:A_{2}=a^{2}:b^{2}\), where \(a = 3\) (side - length of the smaller pentagon) and \(b = 6\) (side - length of the larger pentagon). Then \(A_{1}:A_{2}=3^{2}:6^{2}\).

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Answer:

\(1:4\)