How to find base and height of equilateral triangle if given only area?

An equilateral triangle - means that all sides are the same length

Area of equilateral triangle = (s^2 * root 3) / 4

if area = 60 root 3

60 root 3 = (s^2 * root 3) / 4

(60 root 3) * 4 = s^2 * root 3

s^2 = ((60 root 3) * 4) / root 3

s^2 = (240 root 3 ) / root 3

s^2 = 240

s= root 240

s= 4 root 15

so the side measurements are = 4 root 15

to find height

opposite = 4 root 15 / 2 = 2 root 15

hypotenuse = 4 root 15

a^2 = b^2 + c^2

c^2 = a^2 - b^2

c^2 = (4 root 15)^2 - (2 root 15)^2

c^2 = 240 - 60

c^2 = 180

c = root 180

c= 6 root 5

height = 6 root 5

Hope this Helps!

The area (A) of an equilateral triangle with sides s is

A = (√3)s²/4

or

area = (1/4) * sqrt(3) * s²

You don't need to know the base or height when using this equation. The (1/2)bh formula is for a right triangle. It will work in this case if you know that all the angles in an equilateral triangle are 60 and using trigonometric functions within the area calculation - lots of unnecessary work. Just use the formula above to get your answer. This only works for an equilateral triangle.

The area of a triangle = (base x height ) / 2

An equilateral triangle is a 2D shape so doesn't have a height.