Divide a hexagon into thirds by drawing two lines, one on the inside and one on the outside. The length of these lines is equal to 1/3 of the length of the hexagon’s perimeter.

Connect these lines with a curved line that goes through all six corners of the hexagon. This curve is called an apothem (the plural is apothems). The radius of this curve will be the same as one side of your equilateral triangle, which is also 1/3 of the length of the hexagon’s perimeter.

Draw another curved line that connects two opposite corners with each other. This second curve is called an excircle (the plural is excircles) and its radius will be equal to 1/2 of one side of your equilateral triangle, which is also 1/6th of the length of the hexagon’s perimeter.

Last modified: August 11, 2022