Question 113

Find the ratio of shaded area to unshaded area

Solution

Area of a equilateral triangle is $$\frac{\sqrt3}{4}$$*$$a^2$$

Area of a regular pentagon is $$\frac{5}{4}$$*$$\sqrt{1+\frac{2}{\sqrt{5}}}$$*$$a^2$$

Therefore ratio of shaded area to unshaded area = $$\frac{\frac{5}{4}*\sqrt{1+\frac{2}{\sqrt{5}}}}{\frac{5*\sqrt3}{4}}$$.

i.e. $$\frac{\sqrt{1+\frac{2}{\sqrt{5}}}}{{\sqrt3}}$$

therefore our answer is Option 'D'.

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