- 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:
- 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
- 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 = t2 `sqrt(25)` + 10 `sqrt(5)` / 4
3) Heptogon=> regular:
- A 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:
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
Area circle = π × r2
Notice that the radius of the circle is 4/2 = 2
Area = 3.14 × 22
= 3.14 × 4
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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