Equilateral Triangle: Height
How to find the height of an equilateral triangle: formula, 2 examples, and their solutions.
Equilateral Triangle
An equilateral triangle is a triangle
whose sides are all congruent.
Its interior angles are also all congruent: 60º.
Formula
h = [√3/2]⋅a
h: Height of an equilateral triangle
a: Side of an equilateral triangle
ExampleSide: 8, h = ?
The given triangle is an equilateral triangle.
Its side is 8.
Its height is x.
Then x = [√3/2]⋅8.
Cancel the denominator 2
and reduce 8 to, 8/2, 4.
So x = 4√3.
Exampleh = 12, Side = ?
The given triangle is an equilateral triangle.
Its side is x.
Its height is 12.
Then 12 = [√3/2]⋅x.
Switch both sides.
Multiply, the reciprocal of √3/2, 2/√3
to both sides.
Then x = 12⋅[2/√3].
Rationalize the denominator √3
by multiplying √3/√3.
12⋅2⋅√3 = 24√3
√3⋅√3 = 3
Then x = 24√3/3.
Cancel the denominator 3
and reduce the numerator to, 24/3, 8.
So x = 8√3.