Question

If the area of the smaller pentagon is 232 m^2, find the value of the larger pentagon

Answer 1

If we have the lenght of the sides, the ratio of the smaller pentagon and the larger pentagon is:

`(28)/(35)=(4)/(5)`

As in the area we work with 2 dimensions, the ratio is:

`((4)/(5))^2=(4^2)/(5^2)=(16)/(25)`

The smaller pentagon has 232 m^2, then:

`(16)/(25)=(232)/(x)`

x represents the area of the larger pentagon

`16x=232\cdot25`
`x=(232\cdot25)/(16)`
`x=362.5`

The area of the larger pentagon is 362.5 m^2