Question

The ratio of the sides of two similar pentagons is 5:9. If the area of the larger pentagon is 429.3 cm2, then the area of the

smaller pentagon is cm2. (A pentagon has 5 sides)
Enter a number answer only.

Answer 1

132.5 cm²

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

`(x)/(25)` =
`(429.3)/(81)` ( cross- multiply )

81x = 10732.5 ( divide both sides by 81 )

x = 132.5

Area of smaller pentagon is 132.5 cm²