The height of an equilateral triangle is 6 cm. Then . . .

Question : The height of an equilateral triangle is 6 cm. Then the area of the triangle is 

a) 9√3 cm²

b) 3√3 cm²

c) 12√3 cm²

d) 17√3 cm²

Doubt by Lakshay

Solution:

Height = 6 cm

We know,
Altitude / Perpendicular Height / Height of an equilateral triangle is given by √3a/2

Height = √3a/2

6 =  √3a/2
12/√3 = a
a = 12/√3 cm
a = 12√3/3 = 4√3 cm

Area of equilateral triangle
=√3a2/4
= √3[4√3]²/4

= √3[48]/4
= √3×12
= 12√3 cm²

Hence, c) would be the correct option.