Question

Area of a square inscribed in the incircle of an equilateral triangle of side a is–

• A. 3a²
• B. $\frac{a^{2}}{2}$
• C. $\frac{a^{2}}{6}$
• D. 6a²

Answer 1

Answer: (C)

$\frac{a^{2}}{6}$

Answer 2

r = $\frac{1}{3}$ × a sin 60° = $\frac{a}{2\sqrt{3}}$

Area of the square = 4 × $\frac{1}{2}$r² =$\frac{a^{2}}{6}$