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:

$\frac{28}{35}=\frac{4}{5}$

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

$(\frac{4}{5})^2=\frac{4^2}{5^2}=\frac{16}{25}$

The smaller pentagon has 232 m^2, then:

$\frac{16}{25}=\frac{232}{x}$

x represents the area of the larger pentagon

$16x=232\cdot25$$x=\frac{232\cdot25}{16}$$x=362.5$

The area of the larger pentagon is 362.5 m^2