Discussion

Explanation:

Suppose side of the hexagon = a.

In trapezium ABCF, CF = 2a and AB = a and R and Q are the mid points of oblique sides.

∴ RQ = (AB + CF)/2 = (a + 2a)/2 = 1.5a

⇒ $\frac{Area\left(∆PQR\right)}{Area\left(Hexagon\right)}$ = $\frac{\frac{\sqrt{3}}{4}{\left(1.5a\right)}^2}{6\times \frac{\sqrt{3}}{4}{a}^2}$ = $\frac{2.25}{6}=\frac{3}{8}$

Hence, option (a).

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