Discussion

Explanation:

Area of shaded pentagon = $\frac{5}{4}$$\left(\sqrt{1+\frac{2}{\sqrt{5}}}\right)a^2$

Area of 5, unshaded equilateral triangles = 5 × $\frac{\sqrt{3}}{4}{a}^2$

∴ Ratio of shaded area to unshaded area = $\frac{{\displaystyle \frac{5}{4}}\left(\sqrt{1+{\displaystyle \frac{2}{\sqrt{5}}}}\right)a^2}{5\times {\displaystyle \frac{\sqrt{3}}{4}}{a}^2}$ = $\sqrt{\frac{1}{3}+\frac{2}{3\sqrt{5}}}$

None of the option is right.

Hence, option (d).

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