Find the area of an equilateral triangle with a side of 8 cm.

Let’s write the formula for the area of ​​a triangle:
S = 1/2 × a × h,
where a is the side of the triangle, h is the height drawn to this side.
In an equilateral triangle, all sides are equal and the angles are equal to each other.
Therefore, the height can be drawn to either side.
The magnitude of each angle of an equilateral triangle is 60 ° (180 °: 3 = 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.
Substituting the expression for h in the formula for the area, we get:
S = 1/2 × a × ((a√3) / 2) = (a²√3) / 4,
Substitute the value of the side a into the formula and find the area:
S = (a²√3) / 4 = (8²√3) / 4 = (64√3) / 4 = 16√3 cm².
Answer: the area of ​​an equilateral triangle is 16√3 cm².