Question

Two corresponding sides of two similar pentagons are 12 cm and 28 cm.

What is the ratio of the areas of the pentagon?

A. 27/343
B. 28/12
C. 12/28
D. 9/49

Answer 1

The area of a pentagon is found through the following formula:


`A = (1)/(4) \sqrt{5(5+2 √(5)) } * s^(2)`

s is equal to the side length.

Plug 12 and 28 into the formula.

A(12) = 247.75
A(28) = 1348.85

Divide the first result by the second result.


`(247.75)/(1348.85)` ≈
`0.1836`

9/49 is equal to this decimal.

The answer is 9/49.