How to Find the Diagonal of a Hexagon

By Jess Kroll
Regular hexagons are found in many structures.

A hexagon is a six-sided polygon. A regular hexagon means that each side of the shape are equal to each other while an irregular hexagon has six unequal sides. The shape has nine diagonals, lines between the interior angles. While there is no standard formula for finding the diagonals of irregular hexagons, for regular hexagons the nine diagonals form into six equilateral triangles, making it easy to determine the length of each diagonal line. If one side of the hexagon is known then all sides are known, and the diagonals is easily calculated.

Determine the length of one side of the hexagon. For regular hexagons, all the sides are equal: Thus, every side is the same length and if one side is known, then all are. The known, or given, is labeled as "g" (given side).

Write out the equation for finding the diagonal of a regular hexagon: d (diagonal) = 2g (given side).

Multiply the known or given side of the hexagon by 2. The product is the length of the diagonal of a regular hexagon.

Although you can calculate the number of diagonals in an irregular hexagon, finding the diagonal measurement of an irregular would require first splitting the hexagon into four triangles. However, if they aren't right triangles, which they aren't likely to be, there isn't a formal for finding the length of the interior side, which would be the diagonal. The Pythagorean Theorem applies only to right triangles. if each side and angle were given along with the area, then the diagonals could be determined, but that's a lot of variables to assume.

About the Author

Jess Kroll has been writing since 2005. He has contributed to "Hawaii Independent," "Honolulu Weekly" and "News Drops," as well as numerous websites. His prose, poetry and essays have been published in numerous journals and literary magazines. Kroll holds a Master of Fine Arts in writing from the University of San Francisco.