Properties of a Hexagon

Nuts have a hexagon shape.

A hexagon has six coplanar line segments connected end to end, forming a closed shape. The polygon gets its name from Greek, a combination of "hex" (six) and "gonia" (angle). The hexagon shape is common in both industry and nature. In industry, standard nuts and bolts have the shape of a hexagon because the parallel sides make it easier to grip with a wrench. In nature, six-sided snowflakes are the most common. Bees build their honeycombs in hexagonal shapes because it creates the most area with least amount of wax.

Angles

For regular polygons, the formula for determining the interior angle is (180*(number of sides) - 360)/(number of sides). For a hexagon, there are six sides, so the interior angle of a hexagon is (180*6 - 360)/6 = 120 degrees. The sum of interior angles is 6*120 = 720 degrees. The exterior angles are 60 degrees, calculated by subtracting the interior angle, 120 degrees, from 180 degrees.

Area

The area of a hexagon is approximated by this formula: 2.598 * (length of segment)^2. The exact area is 1.5 * (length of segment)^2 * cotangent (pi/6). Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159.

Diagonals

The number of distinct diagonals in a polygon is equal to 1/2*(number of sides)(number of sides - 3). Therefore, the number of distinct diagonals inside a hexagon is: 1/2*(6)(3) = 9.

Equilateral Triangles

A triangle has three sides with the sum of its interior angles equal to 180 degrees. A hexagon can be divided up into six equilateral triangles.

References

• Math Open Reference: Polygon
• Math Open Reference: Hexagon
• "Handbook of Mathematical, Scientific, and Engineering Formulas, Tables, Functions, Graphs, Transforms"; Research and Education Association; 1994
• Snowcrystals; A Guide to Snowflakes; Kenneth G. Libbrecht; 1999
• The College of St. Rose; Mathematics in Nature: Bees, Honeycombs, Bubbles and Mudcracks; Jonna Massaroni et. al