# Polygon

## What are Polygons?

• A Polygon is a closed figure made up of lines segments (not curves) in two-dimensions.
• A minimum of three line segments are required for making a closed figure, thus a polygon with a minimum of three sides is known as Triangle.

Depending on the sides and angles, the polygons are classified into different types, namely

• Regular Polygon
• Irregular Polygon
• Convex Polygon
• Concave polygon

### Regular Polygon

If all the sides and interior angles of the polygon are equal, then it is known as a regular polygon.

### Irregular Polygon

If all the sides and the interior angles of the polygon are of different measure, then it is known as an irregular polygon.

### Convex Polygon

If all the interior angles of a polygon are strictly less than 180 degrees, then it is known as a convex polygon. The vertex will point outwards from the centre of the shape.

### Concave Polygon

If one or more interior angles of a polygon are more than 180 degrees, then it is known as a concave polygon. A concave polygon can have at least four sides. The vertex points towards inside of the polygon.

## Classification of Triangles

In our article on  Geometric Shapes, we discussed the polygons with the least number of sides – the Triangle. In this section, we will go through different types of triangles.

• Equilateral triangle – Having all sides equal.
• Isosceles triangle – Having any 2 sides equal.
• Scalene triangle – All 3 unequal sides.

• Acute angled Triangle– Each angle is less than 900
• Right Angled Triangle– Any one angle is 900
• Obtuse Angled Triangle– Any one angle is greater than 900

### An Activity:

• Draw different triangles of any dimensions using squares and measuring scales.
• Measure the length of the sides and note them down.
• You will observe that the sum of any 2 sides of the triangle is Always Greater than the 3rd side.
 An interesting fact about Triangle: Sum of all the angles of the triangle is always equal to $180^{\circ}$ (straight angle)

A Quadrilateral is a polygon having the number of sides equal to four.

The table below gives the comparison of Opposite sides, angles, and diagonals of different Quadrilateral.

 Quadrilateral Opposite Sides All sides Equal Opposite angles equal Diagonal Parallel Equal Equal Perpendicular Rectangle ✔ ✔ ✖ ✔ ✔ ✔ Parallelogram ✔ ✔ ✖ ✔ ✖ ✖ Rhombus ✔ ✔ ✔ ✔ ✖ ✔ Trapezium ✖ (Only one side) ✖ ✖ ✖ ✖ ✖ Square ✔ ✔ ✔ ✔ ✔ ✔

### Polygon: A general comparison

 Polygon No. of Sides No. of Diagonal No. of vertices Interior Angle Triangle 3 0 3 60 Quadrilateral 4 2 4 90 Pentagon 5 5 5 108 Hexagon 6 9 6 120 Heptagon 7 14 7 128.571 Octagon 8 20 8 135 Nonagon 9 27 9 140 Decagon 10 35 10 144 Hendecagon 11 44 11 147.273 Dodecagon 12 54 12 150 Triskaidecagon 13 65 13 158.308 Tetrakaidecagon 14 77 14 154.286 Pentadecagon 15 90 15 156

## Three Dimensional Shape (3-D shape)

• These are the shapes that can be projected on a piece of paper but cannot be drawn on a paper. These shapes are known as solids.
 2-D shape (Polygon) 3-D Shape Edge Edge Vertices Vertices — Faces
• 3-D shapes have Faces as the distinguishing Feature.