A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $6\sqrt{2}\text{ cm}$, then the area of the triangle is 

Given diagonal of square $=6\sqrt{2}\text{ cm}$

$\Rightarrow \sqrt{2}.\text{s}=6\sqrt{2}\text{ cm}$

$\Rightarrow \text{s}=\text{6 cm}$

Perimeter of equilateral triangle $=$ perimeter of square

$\Rightarrow \text{3a}=4\text{s}$

$\Rightarrow \text{3a}=4\times 6$

$\Rightarrow \text{a}=8\text{ cm}$

$\therefore \text{\hspace{0.17em}Area of }\Delta \text{=}\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\mathrm{.8.8}=16\sqrt{3}{\text{\hspace{0.17em}\hspace{0.17em}cm}}^2$