Irregular polygons space those varieties of polygon that execute not have equal sides and also equal angles. In various other words, rarely often rare polygons room not regular. Polygons room closed two-dimensional figures that are created by joining 3 or more line segments through each other. There are two types of polygons, regular and irregular polygons. Let us learn an ext about irregular polygons, the types of irregular polygons, and also solve a few examples for better understanding.

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1.Definition of irregular Polygons
2.Properties of rarely often rare Polygons
3.Types of rarely often rare Polygons
4.Difference in between Irregular and Regular Polygons
5.Irregular polygon Formula
6.FAQs on rarely often, rarely Polygons

Definition of irregular Polygons

Irregular polygons are shapes that do not have actually their sides equal in length and also the angle equal in measure. Hence, they are likewise called non-regular polygons. We endure irregular polygon in our daily life just as exactly how we see constant polygons roughly us. The shape of an rarely often rare polygon might not be perfect like regular polygons yet they room closed numbers with various lengths the sides. Few of the examples of irregular polygons room scalene triangle, rectangle, kite, etc. When the angles and also sides of a pentagon and hexagon room not equal, these two forms are considered irregular polygons. The image listed below shows few of the instances of irregular polygons.


Properties of irregular Polygons

Irregular polygons have a few properties of their very own that identify the shape from the other polygons. The nature are:

An rarely often, rarely polygon go not have equal sides and angles.Irregular polygons can either be convex or concave in nature.Irregular polygons are shaped in a basic and facility way.Irregular polygons space infinitely big in size because their sides space not same in length.

Types of rarely often rare Polygons

There space different varieties of rarely often, rarely polygons. However, we are going to view a couple of irregular polygons that are typically used and known to us. Let's take a look.

Scalene Triangle

A scalene triangle is thought about an rarely often, rarely polygon, together the 3 sides are not of same length and all the three interior angles are also not in same measure and also the amount is equal to 180°. In the triangle PQR, the political parties PQ, QR, and RP space not same to each other i.e. PQ ≠ QR ≠ RP. Also, angles ∠P, ∠Q, and also ∠R, room not equal, ∠P ≠ ∠Q ≠ ∠R. Thus, we have the right to use the edge sum residential or commercial property to discover each inner angle.


Isosceles Triangle

An isosceles triangle is taken into consideration to it is in irregular because all three sides are not equal however only 2 sides space equal. All three angles space not equal however the angles opposite to equal sides are equal come measure and also the sum of the internal angles is 180°. In the triangle, ABC, ab = AC, and ∠B = ∠C. All the three sides and also three angles are not equal.



A rectangle is considered an irregular polygon because only its the contrary sides are equal in equal and also all the inner angles are equal to 90°. In the given rectangle ABCD, the sides abdominal muscle and CD room equal, and also BC and advertisement are equal, abdominal muscle = CD & BC = AD. And, ∠A = ∠B = ∠C = ∠D = 90 degrees. But,

AB ≠ ad or BC

BC ≠ abdominal or CD

CD ≠ advertisement or BC

AD ≠ abdominal or CD

Hence, the rectangle is an rarely often, rarely polygon.


Right Triangle

A right triangle is thought about an irregular polygon together it has actually one angle equal to 90° and also the side opposite come the edge is constantly the longest side. Therefore, the lengths that all three sides space not equal and also the three angles room not of the same measure. In the appropriate triangle ABC, the political parties AB, BC, and AC are not equal to every other. Abdominal = BC = AC, wherein AC > ab & AC > BC. And, ∠x ≠ ∠y ≠ ∠z, where ∠y = 90°.


Irregular Pentagon

A pentagon is considered to it is in irregular as soon as all 5 sides room not equal in length. However, periodically two or 3 sides the a pentagon can have equal sides however it is still considered as irregular.


Irregular Hexagon

A hexagon is considered to it is in irregular once the six sides that the hexagons space not in same length. The measure of every of the interior angles is no equal. By the below figure the hexagon ABCDEF, the opposite sides room equal but not all the sides AB, BC, CD, DE, EF, and also AF are equal to every other. Because the sides room not same thus, the angle will also not be same to each other. Therefore, an irregular hexagon is an rarely often rare polygon.

A polygon can be categorized together a regular and also irregular polygon based on the length of its sides. As the name suggests regular polygon literally method a definite pattern that appears in the constant polygon while on the other hand irregular polygon means there is one irregularity that appears in a polygon. Let united state see the difference between both.

Regular PolygonsIrregular Polygons
The size of the sides of a continual polygon is equal.The size of the political parties of an irregular polygon is no equal.
The measure of all interior angles is equal.The measurement of all inner angles is not equal.
The measurement of all exterior angles is equal.The measure of every exterior angles is no equal.
A polygon the is equiangular and equilateral is referred to as a continuous polygon.A polygon who sides room not equiangular and equilateral is dubbed an rarely often rare polygon.

Calculating the area and also perimeter of rarely often rare polygons have the right to be excellent by using straightforward formulas just as how continual polygons are calculated. Let us look at the formulas:

Area of irregular Polygons

An irregular polygon is a airplane closed shape that does not have actually equal sides and equal angles. Thus, in order to calculation the area of rarely often, rarely polygons, we separation the rarely often, rarely polygon right into a collection of regular polygons such that the formulas for their locations are known. Take into consideration the instance given below.


The polygon ABCD is an rarely often rare polygon. Thus, we can divide the polygon ABCD into two triangles ABC and also ADC. The area that the triangle can be derived by:Area the polygon ABCD = Area that triangle abc + Area of triangle ADC.

Perimeter of rarely often rare Polygons

Polygons that execute not have actually equal sides and also equal angles are referred to as rarely often, rarely polygons. Thus, in bespeak to calculation the perimeter of rarely often, rarely polygons, we include the lengths of every sides the the polygon.

Example: uncover the perimeter the the given polygon.

Solution: as we deserve to see, the provided polygon is an rarely often rare polygon together the size of each side is different (AB = 7 units, BC = 8 units, CD = 3 units, and advertisement = 5 units)

Thus, the perimeter of the rarely often, rarely polygon will be given as the amount of the lengths of all sides of its sides.Thus, the perimeter of ABCD = abdominal + BC + CD + ad ⇒ Perimeter the ABCD = (7 + 8 + 3 + 5) devices = 23 units

Therefore, the perimeter that ABCD is 23 units.

Sum of internal Angles of rarely often rare Polygons

The interior angles that a polygon are those angle that lie within the polygon. Observe the inner angles A, B, and also C in the adhering to triangle. The interior angles in an irregular polygon are not equal to every other. Therefore, to discover the amount of the interior angles of an irregular polygon, we usage the formula the same formula as used for continuous polygons. The formula is: sum of inner angles = (n − 2) × 180° wherein 'n' = the number of sides the a polygon.


Example: What is the sum of the interior angles in a Hexagon?


A hexagon has actually 6 sides, therefore, n = 6

The amount of interior angles of a constant polygon, S = (n − 2) × 180S = (6-2) × 180°⇒ S = 4 × 180⇒ S=720°

Therefore, the sum of interior angles of a hexagon is 720°.

Sum the Exterior angles in rarely often rare Polygons

An exterior angle (outside angle) of any shape is the angle formed by one side and the extension of the nearby side of the polygon. Observe the exterior angles shown in the complying with polygon.


To calculate the exterior angles of an rarely often rare polygon we use comparable steps and also formulas together for continual polygons. The sum of the exterior angle of a polygon is same to 360°. Therefore, the formula is,

Sum that exterior angles = 180n – 180(n-2) = 180n – 180n + 360. Hence, the amount of exterior angles of a pentagon equates to 360°.

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Example 1: If the three inner angles of a quadrilateral space 86°,120°, and 40°, what is the measure up of the fourth interior angle?


We recognize that the amount of the inner angles that an rarely often, rarely polygon = (n - 2) × 180°, whereby 'n' is the variety of sides

Since the is a quadrilateral, n = 4.

Hence, the sum of the interior angles the the square = (4 - 2) × 180°= 360°

Let the 4th interior edge be x.

Therefore, 86° + 120° + 40° + x = 360°

⇒ 246° + x = 360°⇒ x = 360° - 246°⇒ x = 114°

The fourth interior angle is 114°.

Example 2: discover the area that the polygon offered in the image.


Solution: It can be viewed that the given polygon is an rarely often, rarely polygon. The area of polygon deserve to be uncovered by separating the offered polygon right into a trapezium and a triangle whereby ABCE creates a trapezium while ECD develops a triangle. In bespeak to find the area that polygon permit us very first list the offered values:

For trapezium ABCE,Length of abdominal = 4 unitsLength the EC = 7 unitsHeight of the trapezium = 3 unitsThus, the area the the trapezium ABCE = (1/2) × (sum the lengths of bases) × elevation = (1/2) × (4 + 7) × 3⇒ Area that trapezium ABCE = (1/2) × 11 × 3 = 16.5 square units

For triangle ECD,Length the EC = 7 unitsHeight of triangle = (6 - 3) systems = 3 unitsThus, the area of triangle ECD = (1/2) × basic × height = (1/2) × 7 × 3⇒ Area that triangle ECD = (1/2) × 7 × 3 = 10.5 square units

The area that the polygon ABCDE = Area of trapezium ABCE + Area that triangle ECD = (16.5 + 10.5) square units = 27 square units

Therefore, the area of the given polygon is 27 square units.

Example 3: uncover the lacking length the the polygon provided in the photo if the perimeter of the polygon is 18.5 units.

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Solution: It have the right to be viewed that the offered polygon is an rarely often rare polygon. The perimeter that the provided polygon is 18.5 units. The provided lengths of the sides of polygon are abdominal = 3 units, BC = 4 units, CD = 6 units, DE = 2 units, EF = 1.5 units and also FA = x units.

Given that, the perimeter that the polygon ABCDEF = 18.5 units⇒ Perimeter that polygon ABCDEF = abdominal muscle + BC + CD + DE + EF + FA = 18.5 units ⇒ (3 + 4 + 6 + 2 + 1.5 + x) units = 18.5 units. Thus, x = 18.5 - (3 + 4 + 6 + 2 + 1.5) = 2 units