Learn what polygons are? Their types, shapes, formulas in detail are. Practice, given questions for better understanding of the polygons.

1. What are Polygons? [Types, Shapes, Formulas and
Examples]
Learning to design interior and exterior angles of polygons is one of the
most daunting tasks for students during geometry class: teachers and
private math tutors say so. Polygon is a 2D (two-dimensional) geometric
figure constructed with straight lines having a finite number of sides.
Triangle with three sides is the most common example of a polygon.
However, there are plenty of common and uncommon polygon shapes we
see and experience without even knowing.
In this blog post, you will learn everything about polygons, such as their
mathematical definition, shapes, types, properties, real-life examples,
other examples, and many more things in detail. Before we start learning,
here is some interesting information for you. Polygon comes from the
Greek language, in which Poly means ‘many’ and -gon means ‘angle.’

2. Definition of Polygons
Any close two-dimensional shape or plane figure formed with straight line
segments is known as a polygon. Open shapes or curved ones don’t make
a polygon. It’s a combination of two words, which means ‘many sides .’A
polygon comprises many straight-line segments, and the points where
these line segments meet are called corners or vertices, making an angle.
Moreover, the line segments are called edges or sides. The sides of
polygons are not limited, and they could have 3 sides, 11 sides, 44 sides,
or more. It can have as many sides as needed. However, the name of the
polygon will surely change or differ.
Shapes of polygons
Following are the most common geometrical shapes of a polygon. These
all are the perfect shapes and examples of a polygon. However, the
number of sides vary, as given below:

3. Shapes of Polygon Number of Sides
Rectangle 4
Triangle or Trigon 3
Square 4
Quadrilateral or Tetragon 4
Pentagon 5
Octagon 8
Nonagon or Enneagon 9
Hexagon 6
Heptagon or Septagon 7
Decagon 10
n-gon n sides
Hendecagon or Undecagon 11

4. Types of Polygons
Polygons are classified into different types depending on the number of
sides and angles. Following are the types of polygons with details and
examples:
1. Regular Polygon
2. Irregular Polygon
3. Concave Polygon
4. Convex Polygon
5. Simple Polygon
6. Complex Polygon
Regular Polygon
A polygon is regular if all sides and interior angles are equal.

5. For Example: equilateral triangle, square, etc.
Irregular Polygon
A polygon is of irregular type if its sides and interior angles are different
in measure. They are primarily in the shape of a pentagon, hexagon, or a
different shape compared to the regular polygon.
For Example: a rectangle, scalene triangle, kite, etc.
Concave Polygon
A polygon with inward and outward vertices, one or more interior angles
of more than 180 degrees, is a concav e polygon. They have at least four
sides.
Hint: concave has a cave in it means its internal angle will always be
greater than 180°.
Convex Polygon
A polygon will be of convex type if all internal angles are less than 180
degrees. Its vertices are mostly ou twards and are exactly opposite of the
concave polygon.
Simple Polygon
Any polygon with only one boundary is called a simple polygon. Its lines
do not cross over each other.
For Example: a pentagon
Complex Polygon

6. A polygon whose sides cross over or intersect each other is called a
complex polygon. Such polygons are also known as self -intersecting
polygons.
Note: a few polygon rules do not work on the complex polygon.
For Example: antiparallelogram, star, etc.
Angles of Polygons
Mainly the angles of the polygons are categorized into two types:
1. Interior Angles
Any of the two given methods calculates the sum of all interior angles of a
polygon:

7. Sum = (n − 2) π radians
n-gon = (n − 2) × 180°
where,
n = number of sides of the polygon
2. Exterior Angles
The exterior angles are always formed on the outside of a polygon. By
definition, an angle formed by one of the sides of a polygon and the
extension of its adjacent side is known as an exterior angle of a polygon.
Note:
• The sum of an exterior angle and its corresponding interior angle is
always equal to 180°
• Regular polygons’ exterior angles are always equal in measure.
Properties of Polygons
Following are the main properties of polygons based on their shapes,
sizes, angles, vertices, and types:
• All polygons have a 2D shape (closing in a space)
• Polygons are made with straight sides or lines.
• Any shape that includes a curve is not a polygon.
• All regular polygons are also called convex polygons.
• Circles are not polygons.
• Calculate = (n-2) x 180° to find the sum of all interior angles of an
n-sided polygon.
• Polygons have both interior and exterior angles.

8. • Calculate = 360°/n to measure all exteri or angles of an n-sided
regular polygon.
• Use = [(n – 2) × 180°] /n to measure all interior angles of an n -sided
regular polygon.
• Interior angle + exterior angle = 180°
• Exterior angle = 180° – interior angle.
• Apply = n (n – 3)/2 to determine the number of d iagonals in a
polygon.
• n – 2 is the total number of triangles formed in a polygon by joining
the diagonal from its one corner.
Formulas of Polygons
You must learn two basic formulas of polygons such as:
1. Area of Polygons
2. Perimeter of Polygons
Area of Polygons
The area is the amount of region covered by a polygon in a two -
dimensional plane. The formula of the polygon area depends on the type
or shape of the polygon.
Units of Area: (meters)2, (centimeters)2, (inches)2, and (feet)2, etc.
Perimeter of Polygons
Perimeter is the total distance covered by a two -dimensional shape’s
sides or boundary length.

9. Polygon Perimeter = Length of Side 1 + Length of Side 2 + Length of Side
3…+ Length of side N (for an N -sided polygon)
Units of perimeter: meters, cm, inches, feet, etc.
Following are a few polygons with area and perimeter formulas:
• Triangle
Area: ½ x (base) x (height)
Perimeter: a + b + c
• Square
Area: side2
Perimeter: 4 (side)
• Hexagon
Area: 3√3/2 (side)2
Perimeter: sum of all six sides
• Pentagon
Area: ¼ √5(5+2√5) side2
Perimeter: Sum of all five sides
• Rectangle
Area: Length x Breadth

10. Perimeter: 2 (length + breadth)
• Parallelogram
Area: Base x Height
Perimeter: 2 (Sum of pair of adjacent sides)
• Rhombus
Area: ½ (Product of diagonals)
Perimeter: 4 x side
• Trapezoid
Area: 1/2 (sum of parallel side) height
Perimeter: sum of all sides
Frequently Asked Questions and Solved Examples
Question 1: Name seven types of polygons?
Answer: Following are the seven types of polygons:
1. Octagon
2. Quadrilateral
3. Pentagon
4. Triangle
5. Decagon
6. Quadrilateral

11. 7. Hexagon
Question 2: The “STOP” sign board is a regular polygon.
Find the interior angle of this regular hexagonal-shaped
signboard.
Solution:
Total number of sides in a signboard = n = 6
Formula of interior angle of polygon = 180º (n -2) / n
Add values in the formula:
Interior angle = (180º (6-2)) / 6
= (720º) /6
= 120º
Hence, each interior angle of the signboard “STOP” measures 120º.
Question 3: How to calculate the diagonals of a polygon?
Answer: The diagonal of a polygon is measured by n (n – 3) /2, where n is
the sides of the polygon.
Question 4: How many diagonals does a triangle have?
Answer: Triangles do not have diagonals.
Question 5: The playground of a school is in the shape of an octagon, and
the gardener has to place a rope around its perimeter. The sides are 15m,
15m, 8m, 8m, 10m, 10m, 13m, 13m. calculate the total meters of rope the
gardener needs for the perimeter?
Solution:

12. As perimeter is the sum of all sides of a polygo n
Required length of rope = perimeter of the playgroun d
Perimeter = 15 + 15 + 8 + 8 + 10 + 10 + 13 + 1 3
= 92 m
Hence, the total length of the rope required = 92m
Question 6: What does a polygon with 7 sides call?
Answer: 7 sided polygon is called Heptagon, and it has 7 vertices.
Question 7: Is a star a polygon?
Answer: Yes, it is. Star is from the field of geometry, and it is known as a
star polygon.
Table of Polygons
Below is an important table of polygons wi th their number of sides,
vertices, diagonals, and interior angles:
Polygon Number of diagonals Number of vertices Number of sides Interior angles
Triangle 0 3 3 60
Pentagon 5 5 5 108
Hexagon 9 6 6 120
Heptagon 14 7 7 128.571
Octagon 20 8 8 135
Quadrilateral 2 4 4 90
Nonagon 27 9 9 140

13. Decagon 35 10 10 144
Hendecagon 44 11 11 147.273
Dodecagon 54 12 12 150
Triskaidecagon 65 13 13 158.308
Pentadecagon 90 15 15 156
Tetrakaidecagon 77 14 14 154.286
Real-Life Examples of Polygons
We use polygons all day, every day. in fact, in every moment of life in the
form of:
• Floor designs
• Fruits
• Honeycomb
• Traffic signals
• Signboards
• Buildings
• Species of starfish
• Laptop, television, and mobile phones (rectangular -shaped screen)