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.

Result

S2 =  31 dm2

Solution:

S2=(1332)2⋅190≐31 dm2S_2 = \left(\dfrac{ 13}{ 32}\right)^2 \cdot 190 \doteq 31 \ dm^2

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