Understanding Elementary Shapes

Polygon and Polyhedrons

When you think of shapes, what is the most common shape that strikes your mind? For some, it may be a circle while for others it may be a rectangle. But did you know that every shape starts from the most basic line? A line when intersects with another line at a point forms an angle. As the number of lines intersecting each other increases the name of shape changes. A polygon is the final result of more than three lines intersecting with each other at different points, let’s discuss how?

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What is a Polygon?


A polygon is a closed figure and is formed by the intersection of line segments. Now, depending on the number of sides we give each polygon a different name. We already know the basic polygons, triangles, and quadrilaterals.  A triangle is a three-sided polygon whereas a quadrilateral is a four-sided polygon.

Types of Polygons

Depending on the sides polygons may be regular or irregular. A regular polygon is one which has sides of equal length and angles of equal measures. Irregular polygons are the ones which are not regular, that is sides and angles may vary, thence giving an irregular shape to the polygon. Every polygon, no matter what the number of sides is, may be regular or irregular in shape.

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Classification of Polygons

Depending on the  number of sides polygons may be classified as follows:

  • Triangle: A triangle is a three-sided polygon. Depending on the length of sides and measures on angles triangles may be equivalent, isosceles, scalene, acute triangle, obtuse triangle and right-angled triangle.
  • Quadrilateral: The Four-sided polygons are called quadrilaterals. Can you guess the names of commonly known quadrilaterals?
  • Pentagon: The Five-sided polygons are called pentagons.
  • Hexagon: The Six-sided polygons are called Hexagons
  • Heptagon: The Seven-sided polygons are called Heptagons.
  • Octagon: The Eight-sided polygons are called Octagons.
  • Nonagon: The Nine-sided polygons are called Nonagons.
  • Decagon: The Ten-sided polygons are called Decagons.



The shapes we studied above are two-dimensional shapes. Each of these shapes is measured in terms of length and breadth. These shapes are planar in dimensions and miss the height attribute. Now we shall study the three-dimensional counterparts of the shapes studied above. Three-dimensional shapes are those objects which have all the three-dimensions, that is,  length, breadth, and height. These objects are also called solid shapes.

Polyhedrons are three-dimensional polygons. A polyhedron in simpler words is a solid-shaped polygon. An edge is that segment where each of the faces meets while vertices are those points where these edges meet. Two most common polyhedrons are pyramids and prisms.


(Source: geocities)

Pyramids have triangular faces meeting at the vertex while prisms have rectangular faces as part of their lateral surfaces with top and bottom identical polygons.

Can you sight some more commonly sighted polyhedrons? Let us help you with it! A matchbox or an ice-cream cone is an example of a polyhedron.

Solved Examples for You

A bicycle tyre has 20 spokes, the angle between a pair of adjacent spokes is :

  1. 10°
  2. 18°
  3. 20°
  4. 30°

Solution: Option B. A circle is a polygon with infinite sides, but the total angle that forms a circle is 360°. Now as given in the question, the bicycle has 20 spokes, so the angle between each pair of adjacent spokes is 360 ⁄ 20 = 18°

Ques. What is not a polygon?

Ans. Any polygon which is not said to be a regular polygon is known as the irregular polygon. It might have sides of different lengths and each interior angle can be of any measure. These polygons can be convex or concave at the same time. But, all the concave polygons are said to be irregular meanwhile the interior angles are all not the same.

Ques. How do you identify a polygon?

Ans. Polygons are generally 2D objects. Polygons are classified by their number of sides. Many polygons have special names.

Ques. Is rectangle a polygon?

Ans. Polygons are multiple-sided figures. These have sides that are called the line segments. The polygons are called according to the number of sides they have and angles too. The most known polygons are the triangles, the rectangles, and the squares.

Ques. What are the characteristics of a polygon?

Ans. Following are the characteristics of the polygon:

Side – the sides are of the line segments that create the polygon.

Vertex – vertex is a point where 2 sides meet.

Diagonal – a diagonal is a line that is connecting 2 vertices that is not aside.

Interior Angle – an angle made through 2 adjacent sides inside the polygon is said to be an Interior angle.

Exterior Angle – an angle made with 2 adjacent sides outside the polygon is called an exterior angle.

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Then what about complete angle?

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