What is a Hexagon? - Definition, Area & Angles

Lesson Transcript
Instructor
David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

Expert Contributor
Elaine Chan

Dr. Chan has taught computer and college level physics, chemistry, and math for over eight years. Dr. Chan has a Ph.D. in Chemistry from U. C. Berkeley, an M.S. Physics plus 19 graduate Applied Math credits from UW, and an A.B. with honors from U.C .Berkeley in Physics.

A hexagon is a shape with six sides, six angles, and six vertices. Understand the definition of a hexagon, explore regular and irregular hexagons, and learn how to find the area of a hexagon. Updated: 10/03/2021

What Is a Hexagon?

Some shapes are found all across nature, and the hexagon is one of these. A hexagon is a 6-sided, 2-dimensional geometric figure. All of the sides of a hexagon are straight, not curved. Hexagons are found in honeycombs created by bees to store honey, pollen, and larvae. They're even famously found in the interlocking columns of volcanic rock that form the Giant's Causeway in Ireland. While these examples might be the most well-known, hexagons are found in many other parts of nature: the bond-shapes of certain molecules, in crystal structures, in the patterns of turtle shells, and more.

But why hexagons? What's so special about them? Well, it's all a matter of efficiency. If you create a grid of hexagons then the shapes perfectly interlock, with absolutely no gaps. But compared to other shapes that interlock like this, the lines of each hexagon are as short as they can be. Any other interlocking shape will have longer lines. The result of this is that they require less materials to construct and have a lot of compressive strength.

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  • 0:05 What is a Hexagon?
  • 1:07 Regular Hexagons
  • 1:37 Irregular Hexagons
  • 1:56 Finding Area
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Regular Hexagons

A hexagon is an example of a polygon, or a shape with many sides. Hex is a Greek prefix which means 'six.' A regular hexagon has six sides that are all congruent, or equal in measurement. A regular hexagon is convex, meaning that the points of the hexagon all point outward. All of the angles of a regular hexagon are congruent and measure 120 degrees. This means the angles of a regular hexagon add up to 720 degrees, or 6 times 120.

Irregular Hexagons

Irregular hexagons can look quite different. An irregular hexagon also has six sides, but they're not of equal length. The points of irregular hexagons can point inward or outward. When the points of a hexagon point inward, even if only one point is inward, then the hexagon is considered a concave hexagon.

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Additional Activities


Hexagon Construction


Using a compass and ruler, we will construct a six-sided plane figure whose sides are all equal. This is a hexagon.


Equipment


  • Compass
  • Ruler
  • Paper
  • Pencil


Instructions


  1. Draw a circle.
  2. Using trial and error, divide the circumference of the circle into three equal parts by making marks on the circumference.
  3. The three marks on the circumference are the vertices of a triangle. Join the vertices by straight lines with your ruler to form the triangle.
  4. Draw a line from one vertex to the center of the line opposite of it. Extend the line so that it intersects the circle. The intersection of the line with the circle is a vertex that will be the start of another triangle you will construct.
  5. Using trial and error, divide the circumference of the circle into three equal parts by making marks. Join the new vertices to form the new triangle. If you had your compass set to the proper opening from the first triangle, you can just repeat using the old setting. You now have two intersecting triangles.
  6. There are six vertices on the circle. Connect the adjacent vertices with their closest neighbor on the circle. Now you have constructed a hexagon.


construction of hexagon from two intersecting equilateral triangles

hexagon

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