The perimeter

The perimeter of equilateral △PQR is 12. The perimeter of the regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to STUVWX?

Correct answer:

r =  2:3

Step-by-step explanation:

$$\begin{gathered} p_1=12 \\ {a}_1=p_1/3=12/3=4 \\ {p}_2=12 \\ {a}_2=p_2/6=12/6=2 \\ S\dots k{a}^2 \\ k=\sqrt{3}/4\doteq 0.433 \\ {S}_1=a_1^2=4^2=16 \\ {S}_2=6\cdot a_2^2=6\cdot 2^2=24 \\ r=S_1/S_2=16/24\approx 0.6667=2:3 \end{gathered}$$

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