# Hexagon

That is, the hexagon is a polygon with six sides, which is more complex than a pentagon or a quadrilateral.

It should be noted that a polygon is a two-dimensional figure drawn by a group of successive non-collinear segments that form a closed space.

## Hexagon elements

Taking the image below as reference, the elements of the hexagon are the following:

• Vertices: A, B, C, D, E, F.
• Sides: AB, BC, CD, DE, EF and AF.
• Interior angles: α, β, , , , . They add up to 720º.
• Diagonals: They are 9 and divided into 3 of each interior angle: AC, AD, AE, BD, BE, BF, CF, CE, DF.

## Hexagon types

According to its regularity, we have two types of hexagons:

• Regular: All its sides are equal and its interior angles are also identical and measure 120º, which adds up to 720º.
• Irregular: Its sides have different lengths and its angles also measure differently.

## Perimeter and area of a hexagon

To better understand the properties of a hexagon, we can calculate its perimeter and area:

• Perimeter (P)The six sides of the polygon are added, i.e.: P = AB + BC + CD + DE + EF + FA. If the hexagon is regular and all sides measure a, then P = 6a is observed.
• Area (A): We can distinguish two cases. If it is an irregular hexagon, we could divide the figure into several triangles, as we see in the drawing below. So, given the length of the diagonals as data, we can calculate the area of each triangle (following the steps explained in the triangles article) and do the summation.

In the example above, we could calculate the area of the triangles ABF, BFE, BCE and CDE.

On the other hand, if the hexagon is regular, we can divide the figure into six equilateral triangles, as we see in the picture below:

So we remember that the area of an equilateral triangle can be determined according to the Heron formula, where s is the half perimeter (P / 2) and the lengths of the sides a, b and c. That is, a = b = c, so the perimeter is 3a (a + b + c).

So A is the area of an equilateral triangle, where the length of its sides is the variable a. Then we can multiply the above formula by six to find the area of the hexagon (A with index h), where the measure of its sides is also the unknown to.

## Hexagon Example

Suppose we have a regular hexagon with side length of 10 meters. What is the perimeter and the area of the figure?