Middle School

The ratio of the sides of two similar pentagons is 5:9. If the area of the larger pentagon is 429.3 cm\(^2\), then the area of the smaller pentagon is ___ cm\(^2\).

Enter a number answer only.

Answer :

Answer:

132.5 cm²

Step-by-step explanation:

Given the ratio of 2 similar figures = a : b, then the

ratio of areas = a² : b²

Here the ratio of sides = 5 : 9, thus

ratio of areas = 5² : 9² = 25 : 81

Let x be the area of the smaller pentagon then by proportion

[tex]\frac{x}{25}[/tex] = [tex]\frac{429.3}{81}[/tex] ( cross- multiply )

81x = 10732.5 ( divide both sides by 81 )

x = 132.5

Area of smaller pentagon is 132.5 cm²

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