Question

Show that the area of an equilateral triangle is under root 3 by 4 x square where X is a side of a triangle

Answer 1

Now apply the Pythagorean theorem to get the height (h) or the length of the line you see in red

a2 = (a/2)2 + h2

a2 = a2/4 + h2

a2 − a2/4 = h2

4a2/4 − a2/4 = h2

3a2/4 = h2

h = √(3a2/4) 

h = (√(3)×a)/2

Area = (base × h)/2 

base × h = (a × √(3)×a)/2 = (a2× √(3))/2

Dividing by 2 is the same as multiplying the denominator by 2.