Irregular and Regular Shapes

  • Regular shapes have all sides equal and all angles equal.
  • Irregular shapes will not have all sides are equal and all angles are equal.
  • A regular shape is denoted as when all the sides of the shapes having same length and the angle value should be equal for all the angles and mostly a two dimension structure is called a "regular" or equilateral shape.
  • For example a Square is a regular shape.

Representation of Irregular and Regular Shapes:


The following shapes are regular based structures, they are

1  ) Hexagon=> Regular:

irregular and regular shapes


  • In mathematics, a hexagon is one of the regular shapes; it has six edges and six vertices. .
  • A regular hexagon has formed by six equilateral triangles.

2) Pentagon: Regular

irregular and regular shapes1


  • A pentagon is a polygon which has five sides, it has five equal sides. A pentagon can be drawn like a self-intersecting figure.
  • The sum of the interior angle for the pentagon should be equal to 540o.

The area of a regular convex pentagon is represented by

A = t`sqrt(25)` + 10 `sqrt(5)` / 4

3) Heptogon=> regular:

irregular and regular shapes c



  • heptagon is a polygon, and it has seven equal sides and seven equal angles. In regular heptagon, the sides are meeting exactly at an angle of 5π/7 radians, which means 128.5714286 degrees.

The area A of a regular heptagon is represented as

                  A = 7/4 a2cot π.


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Representation for Irregular Shapes:


Definition of Irregular shapes:

  • Irregular shapes are shapes which is normally opposite of regular quadrilateral which represents the sides and the angles are totally different.
  • Given below is an example for irregular shape.
  • Example1:) Find the area of the irregular shape for the given problem:

irregular and regular shapes x


Inductive and Deductive Reasoning

The above figure has two shapes, like a square and half a circle
Find the area for each of those two shapes and add the results
Area  = s2
          = 42
          = 16
Area circle = π × r2
Notice that the radius of the circle is 4/2 = 2
Area  = 3.14 × 22
          = 3.14 × 4
          = 12.56
Since we have only half a circle, here we have to multiply the result by 1/2,we get
1/2 × 12.56 = 6.28 
Area of this shape = 16 + 6.28 = 22.28.


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