The length of diagonal of a square is 9√2 cm, the square is reshaped to form a triangle. What is the area (in cm2) of largest incircle that can be formed in that triangle?

Answer: Option C

a√2 = 9√2
a = 9

a + b + c = 36
Circle of maximum radius is only exist in equilateral Δ
3a = 36
a = 12
$$\begin{array}{rl}& S=\frac{a+b+c}{2},\\ & r=\frac{\frac{\sqrt{3}}{4}\times a^2}{\frac{12+12+12}{2}}\\ & \Rightarrow r=\frac{\sqrt{3}}{4}\times \frac{12\times 12\times 2}{36}\\ & \Rightarrow r=2\sqrt{3}\end{array}$$
∴ Area of circle = πr² = 12π