Similarity n-gon

6-gones ABCDEF and A'B'C'D'E'F' are similar. The area of 6-gon ABCDEF is S₁=248 m², and the diagonal length FA is 28 m. Calculate the area of the 6-gon A'B'C'D'E'F' if F'A' = 36 m.

Correct answer:

S₂ =  410 m²

Step-by-step explanation:

$$\begin{gathered} S_1=248{\text{m}}^2 \\ {d}_1=28\text{m} \\ {d}_2=36\text{m} \\ r=\frac{d_2}{d_1}=\frac{36}{28}=\frac{9}{7}\doteq 1.2857 \\ {S}_2=r^2\cdot S_1=1.2857^2\cdot 248=410{\text{m}}^2 \end{gathered}$$

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