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Polygon Definition, Types, Formula And Examples

Polygon Definition, Types, Formula And Examples

Polygons are 2-dimensional shapes made up of straight lines and enclosed within sides. Read the detailed article for more information about Polygon Definition, Types, Formula And Examples.

Polygon

Polygons are 2-dimensional shapes made up of straight lines and enclosed within sides. Polygon means 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 the article given below.

Polygon Definition

A polygon is an enclosed shape with straight lines. 2-dimensional shapes like Rectangles, squares, etc are categorized under polygons. 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.

The below figures show Regular and Irregular Polygons:

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

The sum of exterior angle = 360.

Question-based on polygons

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