We want to find the area of a given regular polygon. Note that a regular polygon with 3 sides is a an equilateral triangle. In such a triangle all sides are congruent and all angles have the measure 60^(∘).
The area of a triangle is half the product of its side and its height. Notice we are given the side but we are missing the height.
See that the height bisects both the vertex angle of the triangle and the opposite side of the vertex, which is a side of the equilateral triangle. As a result, a 30^(∘)-60^(∘)-90^(∘) triangle is created. The length of its shorter leg is 8÷ 2=4in.
In this type of special triangle the length of the longer leg, which is also the height of the larger triangle, is sqrt(3) times the length of the shorter leg.
Longer Leg: sqrt(3)* 4= 4sqrt(3)in.
Therefore, the height is 4sqrt(3) inches.
Let's substitute the height and the base into the formula for the area of a triangle and simplify.
