Area = 1/2 * base + height = 81 √3
Find the relation between the base and the height:-
The triangle formed by the perpendicular from a vertex to the base is a 30-60-90 triangle where the ratio of its sides is 2:1:√3 where 2 is hypotenuse, height is √3 and 1 = 1/2 base of the equilateral triangle. So here we can let 1/2 base = x then height = √3x.
So 81 √3 = x * √3x
x^2 = 81
and x = 9 and the hypotenuse = 2*x = 2x
Therefore the perimeter = 2x * 3
= 6*9
= 54 answer