The Decagon, from recognition to construction.
The Decagon will be introduced to your student around the fifth grade simply for the purpose of identification, and for no other reason. I, however think all kids, should also be taught the connections between the different regular polygons.
These connections mainly are for finding the area and angles of a regular polygon. In a four sided regular polygon (square)the degree value is 360 divided by 4; in a 5 sided regular polygon the degrees are 360/5; in a six sided the degrees are 360/6. The pattern is simply 360 divided by the number of sides of the regular polygon. So even if your child is asked about a 20 sided polygon - they should have by now, developed the skills to know that the angle value will be 360/20.
The steps detailed bellow take you from basic identification of the decagon all the way through to its 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 Decagon?Well it is identified by the number of sides it has.
If the shape you are looking at has 10 sides then it is a 10-gon.
A Regular Decagon is identified by a combination of the number of sides to the shape, the length of the sides AND the size of its angles. It has TEN Sides equal in length ... and TEN Angles equal in size (all are 36 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 Decagon.
To find the area of a Regular Decagon we must know two things:
1: The length of one side and, 2: The perpendicular distance from the center 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 10) 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 shape (constructed in green)
The Area of the decagon is calculated by first finding the area of one of the Isoscoles Triangles created by one side of the decagon, and two lines constructed from the center point to each vertex. Then you multiply this answer by 10, as there are ten of these triangles in the shape. 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 10We have 10 of these triangles in the decagon, so to get its area, we must get the area of ALL 10 triangles.
10 1/2 a r
Ther Perimeter of ANY shape is simply the sum total of all the lengths of the shape - and a decagon is no different.
The perimeter of a Regular Decagon Shape is 10 times the length of one of its sides..
How to construct a Regular DecagonTo 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 ten vertices.
Note:We know that the nine angles of any regualar polygon are equal in size and add to 360 degrees. So each angle is 1/10 of 360 degrees which is 36 degrees.
Step 3: Using your protractor, find the point at 36 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 shape.
Step 4:Using your ruler, measure the length of your decagon 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 shape.
Step 6: Your regular decagon is the shape contained between the ten points of intersection of these nine lines.
Step 7:Using a heavier line connect the ten points to finish your construction.
A quick check to ensure your nonagon shape 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 ShapesAn elementary student is not likely to study any 3d shapes in connection with the decagon. However, there is no harm in your student knowing how to construct a prism and pyramid, using the decagon as the base shape!
Geometric Coloring SheetsThe use of coloring sheets allows your child to start experimenting with polygons of all kinds. 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 regular polygons and other shapes (especially triangles). You will find some nice free geometric coloring pages to download here.
Fun Geometry ProjectsCOMMING SOON!
Theorems & ProofsCOMMING SOON!