If 3 cm is the length of a median of an equilateral triangle, then the area is -

Consider an equilateral triangle ABC having sides a and a median AD of length x unit'.
In an equilateral triangle, the median is always the perpendicular bisector of the triangle.
So, BD=a/2

In triangle ABD, by Pythagoras theorem, we have
AB²=AD²+BD²
⟹a²=x²+(a​/2)²
⟹a²=x²+ a²/4​
⟹3a²​/4=x²
or,a²=4x²/3​

Now, area of equilateral triangle =√3​a²​/4
=​​(√3​​/4) × (4x²/3​)
=√3x²/3

length of a median of an equilateral triangle = 3 cm

so, area of equilateral triangle = √3x²/3 = √3×3²/3 = 3√3 sq cm