# Hexagon

Hexagon is a form of a polygon which consists of six edges and six vertices. And 720◦ is the total of the internal angles of any hexagon.
The hexagon patterns are the most prevalent in the nature due the strong efficiency which they have, if we take on consideration their existence either in bees’ honeycombs or the Giant’s Causeway.
If we talk about hexagonal structures we find that each line in the hexagonal grid is short but in the same time it can be if a large area to fill with the fewest number of hexagons, this mean that it is required less wax by honeycombs to construct and gain lots of strength under compression.
All the internal angles of the regular hexagon are 120◦ and have the same length of all its sides.
It has six lines of symmetry, and the longest diagonals are twice of the length of one side, and which are connecting opposite vertices.
The regular hexagon can be divided into six equilateral triangles, so we can see as triangle with a vertex at the middle of regular hexagon. And the regular hexagon gives the strength and the large space and building materials.
The regular hexagons, like squares and equilateral triangles, fit together without making gaps in the tile of the plane, as well as the reason resides behind the hexagonal shapes of cells of a beehive and makes efficient use of space and building materials.
Although it is equilateral, but it is not considered a triambus:

The upper equation gives the area of a regular hexagon of side length T.
And there is another formula which considered alternative formula for the area where A= 1.5dt and in which the length d is the distance between the parallel sides in the regular hexagon.
The alternative formula and which known flat to flat distance for the area is:

We can find the area by the two formulas:

Any hexagon in the circle is a cyclic hexagon, where all the three main diagonals intersect in a single point.