Correct Answer: $36\sqrt{3}$

Solution :
ABCDEF is a regular hexagon that is divided into 6 equilateral triangles with a side of 12 cm.
We know, Area of a regular hexagon $= 6 × \frac{\sqrt{3}}{4}$ × (side) ² = $ 6 × \frac{\sqrt{3}}{4} ×12^2=216\sqrt3$ cm ²
Area of $\triangle$EOD = area of $\triangle$DOC = $\frac{1}{6}$ × (Area of hexagon) = $\frac{1}{6}×216\sqrt3=36\sqrt3$ cm ²
By symmetry, the area of $\triangle$EGD = the area of $\triangle$CGD = the area of $\triangle$CGO = the area of $\triangle$EGO
⇒ Area of $\triangle$ECD = 2 × area of $\triangle$CGD = the area of $\triangle$COD
= $36\sqrt3$ cm ²
Hence, the correct answer is $36\sqrt{3}$.