Question

If the height of the equilateral triangle is 2√3 cm, then determine the area (in cm2) of the equilateral triangle

Answer 1

Check the attachment

Answer 2

Given :

The height of the equilateral triangle = 2√3 cm

To Find :

The Area of equilateral triangle

Solution :

∵ Area of equilateral triangle = $\dfrac{\sqrt{3} }{4}$ × side²

Height of equilateral triangle =  $\dfrac{\sqrt{3} }{2}$ × side

Now,

∵   height of the equilateral triangle = 2√3 cm

So,  $\dfrac{\sqrt{3} }{2}$ × side =  2√3 cm

Or,    side = $\dfrac{4\sqrt{3} }{\sqrt{3} }$

i.e     side = 4 cm

Measure of each side of equilateral triangle = 4 cm

So, Area of equilateral triangle = $\dfrac{\sqrt{3} }{4}$ × side²

                                                   = $\dfrac{\sqrt{3} }{4}$ × ( 4 cm )²

                                                   = 4√3 sq cm

Hence, The Area of equilateral triangle is 4√3 sq cm  . Answer