The perimeter of an equilateral triangle is 12 cm. Find the height.

Let’s denote the height of an equilateral triangle by h, the length of its side – a.
In an equilateral triangle, all sides are equal and the angles are equal to each other.
The size of each angle is 60 °.
From the definition of sine:
Sin 60 ° = a / h,
h = a × Sin 60 °.
From the trigonometric table: Sin 60 ° = √3 / 2,
h = (a√3) / 2
We are given the perimeter of a triangle, this is the sum of the lengths of its sides.
Since the triangle is equilateral, we find the length of one side:
12: 3 = 4 cm.
Find the height:
h = (4√3) / 2 = 2√3 cm.
Answer: the height of the triangle is 2√3 cm.