A polygon is a closed two-dimensional shape with straight sides. It is a geometric figure that consists of a finite number of line segments (called sides or edges) connected end-to-end to form a closed shape. The sides of a polygon do not intersect each other except at their endpoints. The term polygon comes from the Greek words "poly," meaning many, and "gonia," meaning angle.

Examples of polygons include triangles (three sides), quadrilaterals (four sides), pentagons (five sides), hexagons (six sides), and so on. Polygons can be regular or irregular, depending on whether all their sides and angles are equal or not.

Types of Polygon

Regular polygon

A regular polygon is a polygon that has all its sides of equal length and all its angles are equal.

For example, a regular polygon with three sides is called an equilateral triangle, a regular polygon with four sides is called a square, a regular polygon with five sides is called a pentagon, and so on.

The formula for finding the measure of each interior angle of a regular polygon is given by: Interior angle = [(n-2) × 180^{o}] / n Where n is the number of sides of the polygon.

The formula for finding the sum of interior angles of a regular polygon is given by: Sum of interior angles = 180^{o}(n – 2) Where n is the number of sides of the polygon.

The formula for finding the measure of each exterior angle of a regular polygon is given by: Exterior angle = 360^{o}/n Where n is the number of sides of the polygon.

The formula for finding the number of diagonals of a regular polygon is given by: Number of diagonals = [n(n-3)]/2 Where n is the number of sides of the polygon.

Area of Regular Polygons

The area of area polygon can be calculated using the following formula; A = (n/2) × L × R Where, A = area of the polygon, L = Length of the side n = Number of sides of the given polygon.

Formula for Area of Polygons

The formula for the area of a polygon depends on the number of sides and the type of polygon. Here are some common formulas for different types of polygons:

Irregular Polygon

An irregular polygon is a polygon that does not have all sides or angles equal. In other words, it is a polygon whose sides and/or interior angles are not congruent.

Examples of irregular polygons include scalene triangles, rectangles, parallelograms, and many more.

Irregular polygons are often asymmetrical and do not have the same level of symmetry as regular polygons. Irregular polygons can have any number of sides and angles.

There is no general formula for finding the area of an irregular polygon, as the area formula will depend on the shape and size of the polygon.

We split the irregular polygons to regular and calculate the area based on it.

NOTE: It is important to have the correct measurements and units of measurement when finding the areas of polygons.

Quick Video Recap

In this section, you will find interesting and well-explained topic-wise video summary of the topic, perfect for quick revision before your Olympiad exams.

This is Curio, your AI Doubt Solver. Here to help you with any educational doubts you encounter while preparing for your Olympiad exams. Feel free to ask questions and learn!

Share Your Feedback

CREST Olympiads has launched this initiative to provide free reading and practice material. In order to make this content more useful, we solicit your feedback.

Do share improvements at info@crestolympiads.com. Please mention the URL of the page and topic name with improvements needed. You may include screenshots, URLs of other sites, etc. which can help our Subject Experts to understand your suggestions easily.