A polygon is a closed, two-dimensional figure composed of straight lines in geometry. In most cases, it can quickly be determined by the polygon’s number of sides from its name. A triangle is a polygon that has three sides, for instance. A closed 2-D object with three or more straight lines is called a polygon. A polygon must have three sides at a minimum. At the vertices, each side of the line segment crosses another line segment. A closed, two-dimensional polygon in Mathematics is a shape with straight line segments. It does not have three dimensions. A polygon has flat surfaces throughout. A polygon must have three sides at a minimum. The only location at which a line segment can cross another is at the endpoint. One can quickly determine the shape of a polygon from the number of its sides.
What is Polygon Formula?
The following list includes key Polygon Formula’s:
Formula 1: The sum of an interior polygon’s angles is 180 degrees for regular polygons with n sides (n-2)
Formula 2: [n(n-3)]/2 is the number of diagonals in a “n-sided” polygon.
Formula 3: [(n-2)180°]/n is the measure of each interior angle in a normal n-sided polygon.
Formula 4: A regular n-sided polygon’s outer angle measurement is equal to 360°/n.
The area of a regular polygon is calculated using the formula 5: (number of sides length of one side apothem)/2, where l is the side length and n is the number of sides in the regular polygon.
Formula 6: The area of a regular polygon is given as Area = (Perimeter apothem)/2, where the perimeter equals the number of sides times the length of one side.
Properties of Polygon
The polygon’s crucial characteristics are
- The internal angles of all the quadrangles added together equal 360°.
- A polygon is referred to as concave if at least one of the internal angles is greater than 180 degrees.
- A simple polygon is one that just has one boundary and does not cross over itself. It is a complicated polygon otherwise.
Examples Using Polygon Formulas
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FAQs (Frequently Asked Questions)
1. Is it possible to divide every polygon into triangles?
The most surprising and significant characteristic of triangles is their ability to divide any polygon into triangles by merely drawing its diagonals. This statistic serves as the foundation for understanding why polygonal interior angles sum to 180(n-2) degrees.
2. Is a triangle always a polygon?
Any two-dimensional shape made of straight lines is called a polygon. Polygons include shapes like triangles, quadrilaterals, pentagons, and hexagons. The shape’s number of sides is indicated by the name. A quadrilateral has four sides, whereas a triangle has three. Study material and learning resources on the Polygon Formula are available on the Extramarks website and mobile application.