Digital textbook - Polygons

digital  textbook

Submitted by,

Sandra Faria,

B.Ed Mathematics.

POLYGONS

Contents

TOPICS	PAGE
Polygons	4
Types of Polygons	7
Naming polygons	9
Sum of angles of a Polygon	10

Polygons

A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. The word ‘polygon’ is derived from the greek words ‘poly’ which means ‘many’ and ‘gon’ means ‘angles’.

The name tells you how many sides the shape has. For example, a triangle has three sides, and a quadrilateral has four sides. So any shape that can be drawn by connecting three straight lines is called a triangle, and any shape that can be drawn by connecting four straight lines is called a quadrilateral.

 There are some that wish to name every possible polygon, but there seems a little point in doing so. For example, a 42-sided polygon is called a ‘tetracontakaidigon’.

Beyond about 10 sides, most people call them an ‘n-gon’. For example, a 15-gon has 15 sides. This seems easier to remember and understand.

All of the shapes below are polygons. Notice how all the shapes are drawn with only straight lines? This is what makes a polygon.

If the shape had curves or didn’t fully connect, then it can’t be called a polygon. The orange shape is still a polygon even if it looks like it has an arrow. All the sides are straight, and they are all connected. The orange shape has 11 sides.

Thus, polygons are two dimensional closed shapes and they are made of straight lines.

Now can you answer the following table keeping in mind the properties of a polygon???

Types of Polygons

Now let’s go through some of the common types of polygons. Are you ready for it???

1) Regular or Irregular Polygons

A regular polygon has all angles equal and all sides equal, otherwise it is irregular.

     

2) Concave or Convex Polygons

A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.
If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it)

3) Simple or Complex Polygons

A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself. Many rules about polygons don't work when it is complex.

Naming of Polygons

Sum of angles of a polygon

We know that the sum of angles of a triangle is ________ .

Do we get the same sum for the angles of a quadrilateral?

How about a pentagon?

Thus, the formula for calculating the sum of the interior angles of a regular polygon is (n - 2) × 180° where n is the number of sides of the polygon.

This formula comes from dividing the polygon up into triangles using full diagonals.

Now can you complete the following table…???

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