Question

if the area of equilateral triangle is 36√3cm^2, find its height by herons formula

Answer 1

Area of an equilateral triangle = 81√3 cm2. Let the side of the equilateral trianglebe 'a' cm ⇒ (√3/4) a2 = 81√3 ⇒ (1/4) a2 = 81 ⇒ a2 = 81 x 4 ⇒ a = √(81 x 4) ⇒ a = 9 x 2 ⇒ a = 18. If a side of the a triangle is considered as a base: Area of a triangle = 1/2 x base x height 81√3 = 1/2 x 18 x h 81√3 = 9 x h h = 9√3

Answer 2

area of equilateral triangle  = (root3 * side*side)/4

36root3 = root3*side*side/4

36 = side*side/4

144=side^2

12=side

then 

semi perimeter =(3*12)/2 =36/2 = 18

by heron formula,

root{18*(18-12)(18-12)(18-12)}

root{18*4*4*4}

root{1152}

=24root2

i hope this will help you