Irregular and uneven shapes: What are regular and irregular shapes?

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Irregular Polygons — Definition, Types, Formula

Irregular Polygons Introduction

We know that a polygon is a two-dimensional enclosed figure made by joining three or more straight lines. A regular polygon is a type of a polygon that has equal sides and all interior angles of equal measure. If any one of the conditions is not met, it becomes an irregular polygon. Check out the irregular polygon shapes based on three conditions.

Note that non-polygon shapes are the shapes that do not fulfill the criterion of a polygon. For example: Circle 

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What Are Irregular Polygons?

Irregular polygons are polygons that do not have equal sides and equal angles.

Common examples of irregular polygons are a scalene triangle, kite, rectangle.

The image below shows the difference between a regular hexagon and an irregular hexagon.

Irregular Polygons: Definition

A polygon is said to be an irregular polygon or non-regular polygon if all the sides are not equal in length and and all the interior angles may not be of equal measure.

How to Classify Irregular Polygons

We can classify irregular polygons based on the number of sides. A three-sided polygon is a triangle, a four-sided polygon is a quadrilateral, a five-sided polygon is a pentagon, and so on. Here are a few examples showing the names of irregular polygons and the number of sides:

Properties of Irregular Polygons

Let’s see some properties of irregular polygons.

  1. First, a regular polygon has equal sides and equal angles. If the polygon fails to meet one of these two conditions, it becomes an irregular polygon.
  2. Second, there are irregular polygons having equal sides but unequal angles and vice versa.
  3. In the figure shown below, the shape is a rhombus. Is a rhombus a polygon? Yes, because it is a closed figure made of four line segments. A rhombus is an irregular polygon with equal sides and unequal angles. Its opposite angles are equal but all angles do not have the same measure.

In the above figure, shape B is a rectangle. Now, is a rectangle a polygon? Yes, it is, as it is a closed figure made of line segments. However, it is an irregular polygon with equal angles (90 degrees each) and unequal sides.

Common Types of Irregular Polygons

We will discuss some common irregular polygon examples along with their important properties.

Scalene Triangle

A scalene triangle has three unequal sides. So, it is an irregular polygon.

In the figure, the scalene triangle PQR is an irregular polygon as PQ, QR, and PR are of different lengths.

Isosceles Triangle

An isosceles triangle has two equal sides $(\text{AC} = \text{AB})$ and two equal angles (angle C $=$ angle B). Since the third side and the third angle are not equal to the other two, it is an irregular polygon.


A rectangle ABCD has congruent angles (all angles are right angles), but it does not have equal sides. Since only the opposite sides are equal, a rectangle is an irregular polygon.

Right Triangle

In the right triangle ABC, if the angle B is right angle, the angles A and B will be acute angles (the sum of all angles of a triangle is 180 degrees). Therefore, the three angles cannot be congruent. So, it is an irregular polygon. The following image shows an example of one such right triangle.

Irregular Pentagon

An irregular pentagon is a polygon with five unequal sides. Since it does not have equal sides, it is an irregular polygon.

Irregular Hexagon

An irregular hexagon (or a non regular hexagon) has six unequal sides. So, a non-regular hexagon is an irregular polygon.

Formulas Associated with Irregular Polygons

There are three formulas related to irregular polygons: area formula, perimeter formula, and angle-sum formula. 

Area of Irregular Polygons

Since irregular polygons come in different shapes and sizes, we do not have a standard formula for finding the area of an irregular polygon. So, we can divide it into regular polygons for which the area can be calculated and then we can add them to get the area of an irregular polygon. 

In the following figure, the irregular polygon can be divided into two triangles PQM and RSN, and a rectangle PQRS. 

So, the area of the given irregular polygon $=$ Area of $\angle$PQM $+$ Area of $\angle$RSN $+$ Area of rectangle PQRS

We can find the area of a triangle, provided that the base and height is known, by the formula:

Area of a triangle $= \frac{1}{2}$ base $\times$ height.

Perimeter of Irregular Polygons

To find the perimeter of an irregular polygon, we have to add up the length of all its sides.

Consider the irregular polygon given below. The side lengths are a, b, c, d, e, f, g, h.

Perimeter $= a + b + c + d + e + f + g + h$

Interior Angles and Exterior Angles

When you extend a side of an irregular polygon, the angle formed between the extended side and its adjacent side is the exterior angle. {\circ}$.

Sum of Exterior Angles of Irregular Polygons

For any polygon, regular or non-regular, the sum of its exterior angles is 360 degrees.

Regular Polygons vs. Irregular Polygons

Let’s now compare and contrast regular and irregular polygons.

  1. All sides of a regular polygon are congruent. 

Irregular polygons generally don’t have equal sides. 

Rhombus is an example of an irregular polygon; it has equal sides, but unequal angles.

  1. Regular polygons have equal interior/exterior angles. 

In irregular polygons, the measure of all interior/ exterior angles is not equal. 

A rectangle is an example of an irregular polygon where all the angles are equal but all sides are not of equal length.

  1. Regular polygons have equal sides and equal angles. Conversely, irregular polygons can either have equal sides or equal angles or none.

Solved Examples

1. {\circ}$. So, it is a regular polygon.

Frequently Asked Questions

What are non-polygon shapes?

Non-polygon shapes are figures that do not satisfy the conditions of being polygon. Examples can be a circle and open shapes.

How many triangles are required to form a polygon?

The number of triangles required to form a polygon is equal to the number of sides of a polygon minus two. If the polygon has “n” sides, then the number of triangles in a polygon is $(n – 2)$. For examples, to form a rectangle (which has 4 sides), we need $4 – 2 = 2$ triangles.

What is the difference between an equilateral irregular polygon and an equiangular irregular polygon?

Equilateral irregular polygons are irregular polygons that have equal sides but not equal angles. Conversely, equiangular irregular polygons are irregular polygons with equal angles but not equal sides.

Is a parallelogram a regular polygon?

Parallelograms like rhombus and rectangles are irregular polygons, whereas a square, also a parallelogram, is a regular polygon.

What is the sum of an irregular polygon’s interior and exterior angles at the same corner?

The interior angle and exterior angle of an irregular polygon at the same corner have a sum of 180 degrees (as it falls on a straight line).

  • Polygons
  • Regular Polygons
  • Square
  • Rectangle



5.1 Example 1
5.2 Example 2

A common problem for a surveyor is the calculation of the surface area of a
farmer’s field. The fields are often irregular which makes direct calculation
of their areas difficult. In such case fields are divided into a number of regular
areas (triangles, rectangles, etc.), of which the surfaces can be calculated
with simple formulas. All areas are calculated separately and the sum of these
areas gives the total area of the field.

Figure 29 shows a field with an irregular shape of which the surface area must be determined.

Fig. 29 A field of irregular shape

The procedure to follow is:

Step 1

Make a rough sketch of the field (see Fig. 29a) indicating the corners of the field (A, B, C, D and E) and the field borders (straight lines). In addition some major landmark! are indicated (roads, ditches, houses, trees, etc.) that may help to locate the field.

Fig. 29a A rough sketch of the field

Step 2

Divide the field, as indicated on the sketch, into areas with regular shapes. In this example, the field can be divided into 3 triangles ABC (base AC and height BB,), AEC (base AC and height EE1) and CDE (base EC and height DD1) (see Fig. 29b).

Fig. 29b Division of the field into areas with regular shapes

Step 3

Mark, on the field, the corners A, B, C, D and E with pegs.

Step 4

Set out ranging poles on lines AC (base of triangles ABC and AEC) and EC (base of triangle EDC) (see Fig. 29c) and measure the distances of AC and EC.

Fig. 29c Mark the corners with pegs and set out ranging poles

Step 5

Set out line BB (height of triangle ABC) perpendicular to the base line AC (see Fig. 29d) using one of the methods described in Chapter 4. Measure the distance BB,

Fig. 29d Set out line BB perpendicular to AC

Step 6

In the same way, the height EE, of triangle AEC and the height DD, of triangle CDE are set out and measured (see Fig. 29e)

Fig. 29e Set out line DD1 perpendicular to EC and line EE1 perpendicular to AC

Step 7

The base and the height of the three triangles have been measured. The final calculation can be done as follows:


Triangle ABC: base = AC = 130 m
height = BB1 = 55 m
Triangle ACE: base = AC = 130 m
height = EE1 = 37 m
Triangle CDE: base = EC = 56 m
height = DD1 = 55 m


Area = 0,5 x base x height
= 0. 5 x 130 m x 55 m = 3 575 m2

Area = 0.5 x 130 m x 37 m = 2 405 m
Area = 0.5 m x 56 m x 55 m= 1 540 m²

Field ABCDE:

Area of triangle ABC = 3 575 m2
Area of triangle ACE = 2 405 m2
Area of triangle CDE = 1 540 m2

Total Area = 3 575 m2 + 2 405 m2 + 1 540 m2
= 7 520 m- = 0.752 ha

The surface area of the field shown in Fig. 30 has to be determined at a time that the field is covered by a tall crop (e.g. maize or sugarcane).

Fig. 30 A field covered by a tall crop

The field can be divided into two triangles ABD and BCD (see Fig. 31a). Unfortunately, because of the tall crop, setting out and measurement of the base BD and the two heights AA1 and CC1 is impossible.

Fig. 31a Division of the field in two triangles

In this case, the area of triangle ABD can be calculated using AD as the base and BB1 as the corresponding height. BB1 can be set out and measured outside the cropped area. In the same way, triangle BCD can be calculated using base BC and the corresponding height DD1 (see Fig. 31b).

Fig. 31b Determination of the areas of the two triangles

The procedure to follow on the field is:

Step 1

Mark the 4 corners (A, B, C and D) with ranging poles.

Step 2

Line AD is set out with ranging poles and extended behind A. Line BC is also set out and extended behind C (see Fig. 32a). Measure the distances AD (base of triangle ADB) and BC (base of triangle BCD).

Fig. 32a Measurement of the bases of the two triangles

Step 3

Set out line BB1 (height of triangle ABD) perpendicular to the extended base line AD using one of the methods described in Chapter 4. In the same way, line DD1 (height of triangle BCD) is set out perpendicular to the extended base line BC (See Fig. 32b) Measure the distance BB1 and DD1.

Fig. 32b Measurement of the heights of the two triangles

Step 4

The base and height of both triangles have been measured. The final calculations can be done as follows:


Triangle ABD: base = AD = 90 m
height = BB1 — 37 m

Triangle BCD: base = BC = 70 m
height = DD1 — 50 m


Area = 0.5 x base x height
= 0.5 x 90 m x 37 m = 1 665 m2

Area = 0.5 x 70 m x 50 m = 1 750 m2

Field ABDC:

Area triangle ABD = 1 665 m²
Area triangle BCD = 1 750 m2

Total Area = 1 665 m2 + 1 750 m2 = 3 415 m2
= 0.3415 ha = approx. 0.34 ha

Pearls of irregular shape, uneven

Showroom address: metro station Serpukhovskaya, Bolshaya Serpukhovskaya st. , 14/13, building 1, 3rd floor. There is free parking for cars. We work daily from 10 am to 9 pm. Free admission.

Showroom address: Serpukhovskaya metro station, Bolshaya Serpukhovskaya str., 14/13, building 1, 3rd floor. There is free parking for cars. We work daily from 10 am to 9 pm. Free admission.

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  1. Articles
  2. Irregular pearls

Irregular pearls, also called “Baroque”, sometimes cost even more than perfectly round pearls. At the same time, it is less common. Jewelry with baroque pearls distinguish their owner from all.

The price of jewelry depends on the uniqueness of the shape of pearls, the compatibility of pearls with each other and on the play of light that allows designers to make designer jewelry. In former times, paragon pearls were especially valued, which in shape resembled animals or people’s faces. In recent years, irregularly shaped pearls have gained popularity due to their entry into the casual style. It looks wrinkled, even chewed, it does not have the gloss of the classics, it can be combined with dresses, and with voluminous knitwear, and with jeans. Collecting headsets from such pearls is much more difficult than from round ones.


Among the most famous Baroque pearls is the pear-shaped white La Peregrina, which means “incomparable”. It belonged to Elizabeth Taylor, who received it as a gift from her husband, who bought Peregrine from the Spanish royal dynasty. In turn, she came to the kings during the colonization of America, when one of the slaves exchanged her for freedom.

The reason for the appearance of an irregular shape of pearls is the growth of a mother-of-pearl shell around a grain of sand or an implant near the shell or internal organs of a mollusk, or a diseased condition of an oyster. Freshwater farms are focused on the production of such pearls, but sea pearls also come in bizarre shapes. Jewelers often learn their craft by working irregularly shaped pearls, because they are difficult to spoil, but there are few true masters of baroque pearls: Lydia Courteille and René Lalique are world famous.

The most popular types of baroque pearls

  • Kasumi pearls: drop-shaped with an uneven surface and a thick layer of mother-of-pearl. Very iridescent in color. Size up to 2 cm;
  • Keshi Pearls: Seeds, a by-product of pearl production. If the implant did not take root and was rejected, grains of sand fall into the cavity remaining from it and the oyster continues to build up mother-of-pearl. The resulting pearls are shiny, elegant and do not contain an implant core, that is, they consist entirely of mother-of-pearl. Beads, flower petals for brooches, small designer pendants are made from Kesha;
  • Biwa Pearls: Japanese freshwater pearls with unusual asymmetries — uneven, oblong. Unique in its play of light;
  • Abalone pearls: grows in single shells — abalone. Good for its «gasoline» modulations, dark spots and seams.

Baroque pearls require special care. It is easily scratched, so you need to make sure that the pearls do not touch each other. In the frame, they are usually kept on pins or clips, and the irregular shape prevents a snug fit; care must be taken not to loosen the fasteners. You can only clean with water and soft tissues, chemical and alcohol-containing products can destroy the pearl.

Call +7 (495) 510-70-60, 8 (800) 200-32-63

Arrangement and design of a plot of inconvenient, irregular or uneven shape | DIY

Contents ✓

  • ✓ Variable angle
  • ✓ A room within a room

Sometimes a garden plot has very unfortunate shapes, but if you try , then everything can be corrected by turning its shortcomings into undeniable advantages.

Variable angle

This elongated garden is divided into several individual L-shaped sections with hedges.

If you look at them from different corners of the garden, you get the impression that you have a whole solid fence in front of you, but if you look closely, you can see that in some places other corners of the garden look through it.


This design features strict, straight lines that harmonize perfectly with impeccably even flowerbeds and hedges. Add some tall plants. Use as many natural materials as possible, such as wood.

You will receive:

  • 4 separate lots;
  • changed angle and feeling of walking through a maze;
  • small hedges with openings that let in much more sunlight than an impressive fence;
  • corner in the back yard, behind a partition, in which you can disguise a compost storage.

See also: Plot of irregular shape (narrow, triangular, etc. ) and its layout and landscaping

open and closed spaces L-shaped forms.

2. The L-shape is very convenient for zoning and is easily divided into three square or rectangular parts.

3. In complex cases, don’t be afraid to be creative in choosing the shapes for these parts, bet on their individuality.

4. Partitions arranged in a zigzag pattern divide the garden into parts and visually enlarge the space.


1. Inject a mysterious touch into the smallest corners of your garden by placing secret «courtyards» in their center.

2. Use curved partitions to soften the strict geometric lines of your landscape design.

3. Partitions make the path to your secret room winding.

4. Symmetrical gardens work well with U-shaped partitions.

Room within a room

Create a secluded little corner in the garden where you can enjoy moments of peace and quiet.

Place a small fountain, a statue, or just sit on a bench and enjoy the beautiful view of the flower garden on the opposite wall as a focal point for your eyes.

By alexxlab

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