How to Find the Radius of a Hexagon

By Chance E. Gartneer; Updated April 24, 2017
Find the Radius of a Circle in Mathematics

The radius of a regular hexagon, also called its circumradius, is the distance from its center to its vertexes, or points. Regular hexagons are polygons with six equal sides. The radius length allows the hexagon to be divided into six equal triangles that help in calculating the area of the hexagon. By using the area of the hexagon and the trigonometric properties of the inner triangles, you can find the radius of the hexagon.

Calculate the sine and cosine of 30 degrees and then multiply the two amounts together. The amount of 30 degrees is the measure of the angle between the radius and the apothem, which is the length between the center of the hexagon and the midpoint of a side. The sine of 30 degrees is 0.5 and the cosine of 30 degrees is 0.866. Multiplying the two amounts together results in 0.433.

Multiply the amount calculated in Step 1 by 6. 6 multiplied with 0.433 equals 2.598.

Divide the area of the hexagon by the amount calculated in Step 2. For example, the area of the hexagon is 600. 600 divided by 2.598 equals 230.94.

Calculate the square root of the amount calculated in Step 3 to find the radius of the hexagon. For this example, the square root of 230.94 is 15.197. The radius is 15.197.

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.