By definition, an Equilateral Triangle has all equal angles each 60° and equal sides of the same length.
Draw an Equilateral Triangle with all angles = 60° and each side equal to 1 unit.
Form a height by drawing line through the center of top 60° angle to the bottom side of the triangle
You should split the equilateral triangle into two 30°, 60°, 90° right triangles
A 30°, 60°, 90° right triangle has a set of sides that can be easily found on the internet
The length opposite the 90° angle will be a unit or 1 unit
The length opposite the 30° angle will be half a unit or 1/2 unit (because you split it in half when you dropped the height)
The length opposite the 60° angle, the height, will be √3/2 of a unit or √3/2
The area is still (1/2)*b*h
Whatever your "a unit" represents you have a similar triangle that is proportional to the sides described above.
Look it up, give it a try.
