How do you find the apothem?

Question

a regular hexagon has a side length of 20 how do you find the apothem?

Answer 1

Draw a line from the center of the hexagon to each vertex.  You will have created six triangles. Each central angle is 60 degrees. Since you have 2 equal sides and a 60 degree angle, you can prove that each triangle is equiangular (all angles are equal) and from there you can prove the sides are all equal.

Drawing an apothem creates a 30-60-90 degree right triangle.  Either use the pythagorean theorem to find the apothem length of 10√3 or just use the rules for 30-60-90 degree triangles.

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