**Polygon**

Polygons are 2-dimensional shapes made up of straight lines and enclosed within sides. Polygon meaning all the closed shapes with straight-line figures come under the category of a polygon. You must know about the definition, shape, types, formula and examples of a polygon by reading down the article given below.

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**Polygon Definition**

A polygon is an enclosed shape with straight lines. 2-dimensional shapes like Rectangle, square etc are categorized under polygon. Polygons have a finite number of sides. A circle is not a polygon as it has a curved shape. The points where the 2 straight lines meet are called vertices. The interior is called the body.

**Types of Polygon**

There are mainly 2 types of Polygon:

**Regular Polygon-**The polygon which has equal sides and equal angles. Generally, questions from regular polygon are asked in the exam.**Irregular Polygon-**The one with unequal sides and angles.

Below figures show Regular and Irregular Polygons:

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**Properties of Polygon**

**Polygon:**It is a closed plane figure bounded by three or more than three straight lines.

**Regular Polygon:**All the sides are equal and also all the interior angles are equal

**Sum of Interior angles of a polygon = (n – 2) × 180**

**n → number of sides**

**Sum of exterior angle = 360**

Different Types Of Polygons | ||
---|---|---|

Name |
Sides |
Interior Angle |

Triangle (or Trigon) | 3 | 60° |

Quadrilateral (or Tetragon) | 4 | 90° |

Pentagon | 5 | 108° |

Hexagon | 6 | 120° |

Heptagon (or Septagon) | 7 | 128.571° |

Octagon | 8 | 135° |

Nonagon (or Enneagon) | 9 | 140° |

Decagon | 10 | 144° |

Hendecagon (or Undecagon) | 11 | 147.273° |

Dodecagon | 12 | 150° |

Triskaidecagon | 13 | 152.308° |

Tetrakaidecagon | 14 | 154.286° |

Pentadecagon | 15 | 156° |

Hexakaidecagon | 16 | 157.5° |

Heptadecagon | 17 | 158.824° |

Octakaidecagon | 18 | 160° |

Enneadecagon | 19 | 161.053° |

Icosagon | 20 | 162° |

n-gon | n | (n-2) × 180° / n |

**Important Formulae Related to Regular Polygon :**

The important Polygon formulas have been listed below including the formula for the area of a polygon.

**Question-based on polygons**

**Q1.The ratio between the number of sides of two regular polygon is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons are respectively:**

(a) 3, 6

(b) 5, 10

(c) 4, 8

(d) 6, 12

**Q2. If each interior angle of a regular polygon is 3 times its exterior angle, the number of sides of the polygon is :**

(a) 4

(b) 5

(c) 6

(d) 8

**Q3. A polygon has 54 diagonals. The number of sides in the polygon is :**

(a) 7

(b) 9

(c) 12

(d) 19

**Q4. The ratio between the number of sides of two regular polygon 1 : 2 and the ratio between their interior angle is 3 : 4. The number of sides of these polygons are respectively :**

(a) 3, 6

(b) 4 , 8

(c) 6, 9

(d) 5, 10

**Q5. The sum of all the interior angles of a regular polygon is four times the sum of its exterior angles. The polygon is :**

(a) hexagon

(b) triangle

(c) decagon

(d) nonagon

**Q6. The ratio of the measure of an angle of a regular nonagon to the measure of its exterior angle is :**

(a) 3 : 5

(b) 5 : 2

(c) 7 : 2

(d) 4 : 5

**Q7.The ratio of the measure of an interior angle of a regular octagon to the measure of its exterior angle is :**

(a) 1 : 3

(b) 2 : 3

(c) 3 : 1

(d) 3 : 2

**Q8.The sum of the interior angles of polygon is 1440°. The number of sides of the polygon is :**

(a) 9

(b) 10

(c) 8

(d) 12

**Q9.The sum of all exterior angles of a convex polygon of n sides is :**

(a) 4 right angle

(b) 2/n right angle

(c) (2n – 4) right angle

(d) n/2 right angle

**Q10.One angle of a pentagon is 140°. If the remaining angles are in the ratio 1 : 2 : 3 : 4, the size of the greatest angle is :**

(a) 150°

(b) 180°

(c) 160°

(d) 170°

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