Question

The height of equilateral triangle is 6cm.Find area

Answer 1

the height of triangle is 6cm
then base length is found by pythagoras theorem
$a^{2}= ( \frac{a}{2} )^{2}+ h^{2}$
$\frac{3a^2}{4}=36$
$a^{2}=48$
$a= \sqrt{48}$
The area of the triangle
$= \frac{1}{2}ah =3 \sqrt{48}=20.7846 cm^2$

Answer 2

Height of equilateral triangle is  √3/2 X a, where 'a' is the side of the equilateral triangle. So √3/2 x a = 6.  
Hence a = 12/√3.
   Area of an equilateral triangle is 1/2  base x height
ie   1/2 x 12 ÷ √3  x 6  =  36 ÷√3
  =  12√3.