An equilateral triangle with side length 18 cm is shown in the diagram, work out the height of the triangle.

There are a couple of ways to do this......but.....if we divide the triangle in half with a vertical line, we will have a right triangle with one leg  = 9   and the hypotenuse  =18.....and the height will form the other leg

Using the Pythagorean Theorem  the height, H  =

sqrt ( 18^2 - 9^2)   =  sqrt (243)   = sqrt (81 * 3)  =   9 sqrt(3)  cm