Question

Find the area of an equilateral triangle, if the altitude is 5√3 cm.

Answer 1

If side is a cm, then length of altitude will be
x = √[(a)²-(a/2)²] 
  =√(3a²/4)
  =(a/2)√3
⇒x = (a/2)√3
⇒a = 2x/√3 = 10 cm

Now, area = (√3/4)a²
                 =(√3/4)×(10)²
                 = 25√3 cm²

Answer 2

We have side= 10 cm

So,we know that area of equilateral triangle is area (√3/4)a²
By implying values,                  
=(√3/4)×(10)²
= 25√3 cm²