Let us assume a be the side of the equilateral triangle

We know that,

Area of an equilateral triangle = sq units

It is given that,

Area of the equilateral triangle = 81 cm²

81 cm² = a²

a² = = 324

a = = 18 cm

Height of an equilateral triangle = a

Since, the value of a is 18 cm

Therefore,

Height = × 18

= 9 cm