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Irregular Polygons – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Irregular PolygonsIrregular Polygons – Definition, ExamplesTable of ContentsIrregular Polygons Definition of Irregular Polygons

Irregular polygons are two-dimensional enclosed figures made up of three or more straight lines where not all sides are equal in length and not all interior angles have the same measure. A polygon becomes irregular if it fails to meet one of these two conditions: having equal sides and having equal angles. Common examples of irregular polygons include scalene triangles, kites, and rectangles.

There are various types of irregular polygons classified based on the number of sides. These include triangles (333 sides), quadrilaterals (444 sides), pentagons (555 sides), hexagons (666 sides), and more. Some irregular polygons may have equal sides but unequal angles (like a rhombus), while others have equal angles but unequal sides (like a rectangle). For any irregular polygon with nnn sides, the sum of interior angles is (n−2)×180∘(n - 2) \times 180^{\circ}(n−2)×180∘ and the sum of exterior angles is always 360∘360^{\circ}360∘.

Examples of Irregular Polygons Example 1: Finding the Perimeter of an Irregular Pentagon Problem:

Find the perimeter of the below figure (an irregular pentagon ABCDE with sides AB = 121212 inches, BC = 101010 inches, CD = 666 inches, DE = 444 inches, and AE = 777 inches).

Unequal pentagon

Step-by-step solution:

Step 1, Add up all side lengths to find the perimeter of the irregular pentagon ABCDE.

Step 2, Write out the formula: Perimeter = AB + BC + CD + DE + AE.

Step 3, Substitute the known values: Perimeter = 12+10+6+4+712 + 10 + 6 + 4 + 712+10+6+4+7.

Step 4, Calculate the sum: Perimeter = 393939 inches.

Example 2: Calculating the Area of a Right Triangle Problem:

Find the area of the below right triangle ABC (where AB = 333 cm and BC = 666 cm).

Right triangle

Step-by-step solution:

Step 1, Remember the formula for the area of a right triangle: Area = 12×\frac{1}{2} \times21​× base ×\times× height.

Step 2, In a right triangle, the two sides that form the right angle can be used as the base and height.

Step 3, Substitute the values into the formula: Area = 12×\frac{1}{2} \times21​× BC ×\times× AB = 12×6×3\frac{1}{2} \times 6 \times 321​×6×3.

Step 4, Calculate the result: Area = 999 cm².

Example 3: Counting Exterior Angles in an Octagon Problem:

How many exterior angles are there in an irregular octagon?

irregular octagon

Step-by-step solution:

Step 1, Remember that the number of exterior angles in any polygon equals the number of sides.

Step 2, An octagon has 888 sides.

Step 3, Each side of the polygon forms one exterior angle with the extension of its adjacent side.

Step 4, Since the octagon has 888 sides, it has 888 exterior angles.

Comments(7)WWriterEllaNovember 4, 2025This def of irregular polygons is great! I've used it to help my students grasp the concept. Simple & clear, makes learning easier.

MMagicianKimNovember 4, 2025I've been using this irregular polygons def for my kid's math. It's clear and really helped them grasp the concept. Thanks!

MCMs. CarterSeptember 17, 2025I’ve used the Irregular Polygons page to explain shapes to my kids, and it made such a difference! The examples and step-by-step solutions were super helpful for their math homework.

NNatureLover89September 10, 2025I used this page to help my kids understand irregular polygons for their homework, and it was super clear! The examples and step-by-step solutions made it so easy to explain. Great resource!

MCMs. CarterAugust 27, 2025I’ve been using this definition to help my kids understand irregular polygons, and it’s been so helpful! The examples make it super clear, and we even tried drawing our own irregular shapes together. Great resource!

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