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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
| 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 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°
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