Question

find the height of an equilateral triangle whose side is 12

Answer 1

area of equilateral ∆= √3/4 a²
=√3/4×12×12
36√3 unit²


again area of ∆=1/2×b×h
36√3=1/2×12×h
h=6√3
h=6×1.73
h=10.38 unit

Answer 2

The answer is 6√3

Draw or construct the height of the triangle

Since it is an equilateral triangle, the height and the median are the same

Therefore, the base is divided into 2 equal parts

Take one of the right angled triangle and apply Pythagoras theorem

12^2 - 6^2 = 6√3