Polygons On Basis of Angles
Polygons can be classified based on the nature of their angles into two main categories:
Convex Polygon
A convex polygon has no interior angle that measures more than 180°. Convex polygons can have three or more sides. In convex polygons, all diagonals lie inside the closed figure. Common examples of convex polygons are triangles, all convex quadrilaterals, as well as regular pentagons and hexagons
Concave Polygon
A concave polygon has at least one interior angle that is a reflex angle and points inwards. Concave polygons have a minimum of four sides. This type of polygon features at least one interior angle measuring more than 180°. In concave polygons, some diagonals extend outside the enclosed figure. Examples of concave polygons include a dart or an arrowhead in quadrilaterals, as well as certain irregular pentagons and hexagons.
Difference between Concave vs Convex Polygons
Let’s see the difference between Convex and Concave Polygon in the table below:
Convex Polygon |
Concave Polygon |
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The entire perimeter of a convex shape extends outward without any inward indentations. |
A Concave shape features at least one inward-pointing portion, indicating the presence of a dent. |
In a Convex Polygon, all internal angles are below 180°. |
In a Concave Polygon, there exists at least one interior angle exceeding 180°. |
Any line connecting two vertices of a convex shape lies entirely within the boundaries of the shape. |
The line connecting any two vertices of a concave shape may or may not intersect the interior of the shape. |
Polygon – Shape, Formula, Types, and Examples
Polygon in Maths is a two-dimensional shape made up of straight lines that form a closed polygonal chain. The word “polygon” comes from the words “poly” and “gon”, which mean “many” and “sides”.
Polygons can be simple or self-intersecting. A simple polygon does not intersect itself, except at the shared endpoints of consecutive segments. A polygonal chain that crosses over itself creates a self-intersecting polygon. Polygons can also be classified as concave or convex.
In this article, we have mentioned in detail about Polygons and their types, formulas, and examples.
Important Facts about Polygons |
|
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Sum of Interior Angles of Polygon |
(n–2) × 180° |
Number of Diagonals in Polygon |
n(n–3)/2 |
Interior Angle of Regular Polygon |
{(n–2) × 180°}/n |
Exterior Angle of Regular polygon |
360°/n |
Table of Content
- What are Polygons?
- Polygon Definition
- Polygon Chart based on Number of Sides
- Properties of Polygons
- Polygon Shapes
- Types of Polygons
- Polygons on the Basis of Sides
- Polygons On Basis of Angles
- Polygons On Basis of Boundaries
- Polygon Formulas
- Area of Polygons
- Perimeter of Polygons
- Angles in Polygons
- FAQs
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