Polygons – Explanation, Types, Properties, Angles, Area, Perimeter, and FAQs

Define Polygons

A polygon is a closed plane figure formed by three or more line segments, called sides, that intersect at angles. The segments that connect the sides are called the polygon’s vertices.

Polygon Examples

A polygon is a closed figure with straight sides. A polygon has at least three sides, and the sum of the angles in a polygon is always greater than 180 degrees.

Some common polygon shapes are squares, rectangles, triangles, and circles.

Here are some examples of polygons:

• square
• rectangle
• triangle
• circle
• Polygon Examples with Sides

There are a few different ways to define a polygon. The most basic is a closed plane figure with at least three points, called vertices, and no more than four sides. The sum of the angles in a polygon is always 180 degrees.

• A triangle has three sides and three angles. The sum of the angles in a triangle is always 180 degrees.
• A quadrilateral has four sides and four angles. The sum of the angles in a quadrilateral is always 360 degrees.
• A pentagon has five sides and five angles. The sum of the angles in a pentagon is always 540 degrees.
• A hexagon has six sides and six angles. The sum of the angles in a hexagon is always 720 degrees.
• A heptagon has seven sides and seven angles. The sum of the angles in a heptagon is always 900 degrees.
• An octagon has eight sides and eight angles. The sum of the angles in an octagon is always 1080 degrees.

Three-Sided Polygons or Triangles

Three-sided polygons are called triangles. The sum of the angles in a triangle is always 180 degrees.

Four-Sided Polygons or Quadrilaterals

• A square is a four-sided polygon with four right angles.
• A rectangle is a four-sided polygon with two pairs of parallel sides.
• A rhombus is a four-sided polygon with four equal angles.
• A parallelogram is a four-sided polygon with two pairs of parallel sides.

Types of Polygon

• A polygon is a plane figure that is bounded by a finite number of straight line segments.
• A polygon is a plane figure that is bounded by a finite number of straight line segments. The segments meet at points called vertices. The points where two segments meet are called corners or angles. The number of corners is called the polygon’s degree.
• A polygon has at least three sides. A polygon with three sides is called a triangle. A polygon with four sides is called a quadrilateral. A polygon with five sides is called a pentagon. A polygon with six sides is called a hexagon. A polygon with seven sides is called a heptagon. A polygon with eight sides is called an octagon. A polygon with nine sides is called a nonagon. A polygon with ten sides is called a decagon.
• There are also polygons with more than ten sides. A polygon with eleven sides is called a undecagon. A polygon with twelve sides is called a dodecagon. A polygon with thirteen sides is called a tridecagon. A polygon with fourteen sides is called a tetradecagon. A polygon with fifteen sides is called a pentadecagon. A polygon with sixteen sides is called a hexadecagon. A polygon with seventeen sides is called a heptadecagon. A polygon with eighteen sides

Types of Polygons and its Properties

There are a few types of polygons that are the most common. Here is a list of them with a brief description of each:

Triangle: A three-sided polygon.

• A three-sided polygon. Quadrilateral: A four-sided polygon.
• A four-sided polygon. Pentagon: A five-sided polygon.
• A five-sided polygon. Hexagon: A six-sided polygon.
• A six-sided polygon. Heptagon: A seven-sided polygon.
• A seven-sided polygon. Octagon: A eight-sided polygon.
• A eight-sided polygon. Nonagon: A nine-sided polygon.
• A nine-sided polygon. Decagon: A ten-sided polygon.
• A ten-sided polygon. Polygon: Any closed figure made of straight lines that connects a finite number of points.

The shapes of polygons are described by their number of sides, angles, and vertices.

Properties of Polygons

• A polygon is a closed figure consisting of a finite number of straight line segments, called its sides, connected end to end.
• The segments joining the sides are called the angles of the polygon.
• The polygon is said to be regular if all the angles are equal and all the sides are equal.
• A polygon is said to be irregular if at least one of the angles is not equal to the others or if at least one of the sides is not equal to the others.
• The sum of the angles of a polygon is always 360°.
• The interior angles of a polygon add up to 360°.
• A polygon is convex if it has at least one interior angle that is less than 180°.
• A polygon is concave if it has at least one interior angle that is greater than 180°.

Angles of Polygons

• The sum of the angles in a polygon is always 180°.
• The measure of each angle in a polygon is determined by its location within the polygon.
• The interior angles of a triangle add up to 180°.
• The interior angles of a quadrilateral add up to 360°.
• The exterior angles of a polygon are the angles formed by the intersection of two adjacent lines. The exterior angle of a triangle is equal to the sum of the other two exterior angles.

Interior Angle Property of a Polygon

The interior angle property of a polygon states that the sum of the angles inside a polygon is always equal to 180 degrees.

Exterior Angle Property of a Polygon

The exterior angle of a polygon is the angle formed by two consecutive sides of the polygon.

Area and Perimeter Formulas of Polygons

A polygon is a closed figure with straight sides. The area of a polygon is the number of square units it takes to cover the polygon. The perimeter of a polygon is the distance around the polygon.