About the Hexagon Shape, from recognition to construction.
The Hexagon Shape is one of the shapes your Kindergartner learns to identify as part of their math curriculum. But what catches most elementary students out at some point are the two terms - Hexagon and Regular Hexagon. I feel the reason for this is that the shape above is a Regualr Hexagon, but most kids learn to identify it as simply a Hexagon. Is this wrong? No. It is a Hexagon. But a Hexagon is ANY shape composed of 6 intersecting lines. A regular hexagon is a 6 sided shape where ALL lines are the same length and ALL angles are equal in size. You can investigate more Regular Polygons in more detail another time.
The steps detailed bellow take you from basic identification all the way through to construction and more! These steps also include 'pit stops' to complete fun geometry projects and coloring sheets.
These are nice 'breathers' on the learning curve, but they are excellent ways of reinforcing the new knowledge in ways that your kid can get a real life, hands on approach to understanding the basic geometry concepts included.
Okay, so let's get started ...
How do we know what we look at is a Hexagon Shape?A Hexagon Shape is identified by the number of sides it has.
It has SIX sides.
The Regular Hexagon is the Hexagon Shape that is studied by students at the elementary level.
A Regular Hexagon is identified by a combination of the number of sides to the shape, the length of the sides AND the size of its angles. A Regular Hexagon has Six Sides equal in length ... and Six Angles equal in size (all are 60 degrees at the center). The internal angles (those at the vertices, but inside the shape are 120 degrees.
Once your child is comfortable with how to recognize this shape, offer them a shape worksheest to see how they get on with identifying it.
Calculate Area and Perimeter
How to calculate the Area and Perimeter of the Regular Hexagon Shape.
To find the area of a Regular Hexagon we must know two things:
1: The length of one side and, 2: The perpendicular distance from the center of the hexagon to one of its sides. (In 'math speak' this perpendicular distance is known as the APOTHEM!) In my diagram I have included 2 (there is a total of 6 in a hexagon) and these are the blue lines. You can also see that these Apothem's are in fact the radius of a circle inscribed in the hexagon (constructed in green)
The Area of the hexagon is calculated by first finding the area of one of the Isoscoles Triangles created by one side of the hexagon, and two lines constructed from the center point to each vertex. Then you multiply this answer by 6, as there are six of these triangles in a hexagon. These construction lines are in Orange in my diagram.
Step 1: Area of Isoscoles Triangle Area of any triangle is half its base multiplied by it perpendicular height. In this case
1/2 a r
Stpe 2: Multiply by 6We have 6 of these triangles in the Hexagon, so to get the area of the hexagon, we must get the area of ALL six triangles.
6 1/2 a r
6/2 a r
These questions can be presented in many different ways, depending on the grade level of your child. For example, if your child is just learning about area (perhaps second or third grade) they could be given the area of one of these trianles. To solve this, they would simply multiply the area given by 6. If on the other hand, your child is in 4th grade, they will probably be given a question which has a solution similar to the explanation above. But what about a 6th grader? These students could possibly be given information that will require a more complicated solution. And complicated solutions demand an understanding of what is happening, not just a 'plug and play' system with a formula. For example, they could be given the above question, but instead of being given the value of 'r', perhaps they are given the vlaue of the orange construction lines! What then? Would your student see the 12 right angled triangles, rather than the 6 isosoceles? Would they make the connection to the Theorem of Pythagoras to find the length of 'r'?
These are good examples of how a shape can be studied all the way through 7 grades, and still get more and more difficult. The difficult isn't 'tricks' put out there to make a childs life miserable, they are there to ensure a solid understanding. The only way any student can gain this level of understanding is through practice.
Ther Perimeter of ANY shape is simply the sum total of all the lengths of the shape - and a heagon shape is no different.
The perimeter of a hexagon is 6 times the length of one of its sides..
How to construct a Hexagon ShapeTo complete this, you will need a ruler, pencil, protractor, and a blank piece of paper!
Approach 1: Using a protractor
Step 1: Draw a straight line lightly using your ruler and pencil on your paper. - This is what we call a construction line.
Step 2: Indicate on this line, one point - this point will be the first of the six vertices.
Note:We know that the six angles of any regualr hexagon are equal in size and add to 360 degrees. So each angle is 1/6 of 360 degrees which is 60 degrees.
Step 3: Using your protractor, find the point at 60 degrees to your first line using the point you indicated as the base, mark it, and draw another construction line.
You now have two lines of your hexagon.
Step 4:Using your ruler, measure the length of your hexagon side on BOTH of these lines, and mark with a point. Step 5:Using these new points, repeat Step 3: until you have completed your hexagon shape.
Step 6: Your hexagon is the shape contained between the six points of intersection of these six lines.
Step 7:Using a heavier line connect the six points to finish your construction.
A quick check to ensure your hexagon is accurate, is to measure all side lengths with your ruler. If you have done it correctly all sides will measure the same!
Relationship to 3D ShapesThe 3d Figures a Kindergarten through sixth grade student is most likely to deal with are the Hexagonal Pyramid, and Hexagonal Prism.
Geometric Coloring SheetsThe use of coloring sheets allows your child to start experimenting with hexagons. A great first step is to encourage your child to color in shapes adjacent to eachother with the same color, until their shape starts to look like 'something'. By doing this, your child will start to realize the connection between the hexagon and other shapes (especially triangles). You will find some nice free geometric coloring pages to download here.
Fun Geometry ProjectsCOMMING SOON!
Theorems & ProofsCOMMING SOON!