# Get the Knowledge that sets you free...Science and Math for K8 to K12 students

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## Polygons

Scallop shell A good real life example of polygon is a scallop shell. The polygon formed in the above figure is 16-sided. Can you identify the number of diagonals from the vertex A and the total number of diagonals possible?

A closed plane figure bounded by three or more line segments is called a polygon. The line segments forming a polygon are called its sides and the point of intersection of two consecutive sides of a polygon is called a vertex. The number of vertices of a polygon is equal to the number of its sides.

Diagonal of a polygon: A line segment joining any two non–consecutive vertices of a polygon is called its diagonal. Thus, in the above figure, ABCDEF is a polygon and each of the line segments AC, AD, AE, BD, BE, BF, CE, CF and DF is a diagonal of the polygon.

The number of diagonals from any one vertex for a 'n' sided polygon is given by: (n – 3). Isn't it?

Regular polygons All the sides of a regular polygon are equal.
Naming a Polygon

Polygons are named according to the number of their sides.

No. of sides Name of the polygon No. of sides Name of the polygon
3 Triangle 9 Nonagon
5 Pentagon 11 Undecagon
6 Hexagon 12 Dodecagon
7 Heptagon 13 Tridecagon
8 Octagon n n–gon
STOP sign A practical example of a convex polygon is a STOP sign. Since it has 8 equal sides, it is called an regular octagon. All the interior angles are equal and each is less than 180°.

Starfish
Starfish is a good real life example of a concave polygon. It has 10 sides and hence a decagon. All the sides are equal. But a concave polygon can not be called regular because of the reflex angle. In the starfish there are 5 reflex angles.
Convex and Concave Polygons

Convex polygon: If each angle of a polygon is less than 180° (straight angle), then it is called a convex polygon. All the diagonals of a convex polygon lie entirely inside the polygon. In the below figure, ABCDEF is a convex hexagon.

Concave polygon: If at least one angle of a polygon is more than 180° (reflex angle), then it is called a concave polygon. In concave polygon, a line segment joining any two points in the interior does not lie completely within the figure. In the below figure, ABCDEFG is a concave heptagon.

Regular polygon: A polygon in which all sides are equal and all angles are equal is called a regular polygon. You will come to know that all exterior angles are also equal.