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.
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 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.
Like all regular shapes, there's a simple formula we can use to calculate the area of a hexagon. The formula for the area of a regular hexagon looks like this:
Where s is the length of one of the sides of the hexagon. Simply plugging the length of one of the sides into the equation, and typing it into a calculator, gives you the area of the hexagon.
So, for example, if you have a regular hexagon where each side is 5 centimeters long, you would multiply three-root-three, by five squared, and divide the answer by two. That will give you 65 centimeters squared. If you used a different unit for the length of the side, like meters for example, the answer would be in meters squared. And, that's all there is to it.
A hexagon is a polygon with 6 straight sides. It's commonly found in nature, because it's a particularly efficient shape. A regular hexagon has sides that are all congruent and angles that all measure 120 degrees. This means the angles of a regular hexagon add up to 720 degrees. You can find the area of a hexagon by using the measurement of one of the sides and the area formula:
An irregular hexagon has sides that are not the same measurement and can have points facing inward as well as outward. A hexagon with even one inward point is considered to be a concave hexagon.
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Using a compass and ruler, we will construct a six-sided plane figure whose sides are all equal. This is a hexagon.
- Draw a circle.
- Using trial and error, divide the circumference of the circle into three equal parts by making marks on the circumference.
- 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.
- 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.
- 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.
- There are six vertices on the circle. Connect the adjacent vertices with their closest neighbor on the circle. Now you have constructed a hexagon.
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