In an equilateral ΔABC, the medians AD, BE and CF intersect to each other at point G. If the area of quadrilateral BDGF is 12√3 cm², then the side of ΔABC is:

Solution (By Examveda Team)

$$\eqalign{ & 2{\text{ unit}} \to 12\sqrt 3 \cr & 6{\text{ unit}} \to 12\sqrt 3 \times 3 = 36\sqrt 3 \cr & {\text{Area}} = \frac{{\sqrt 3 }}{4}{a^2} \cr & 36\sqrt 3 = \frac{{\sqrt 3 }}{4}{a^2} \cr & a = 12{\text{ cm}} \cr} $$