Similarity n-gon

9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S₁=190 dm² and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm.

Correct result:

S₂ =  31 dm²

Solution:

$S_2={\left({\displaystyle \frac{13}{32}}\right)}^2\cdot 190\doteq 31{\text{dm}}^2$

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