What is a Polygon? Shape, Types, Formulas, Examples, Facts

what is a polygon?

In geometry, a polygon can be defined as a flat or two-dimensional closed shape bounded by straight sides. it has no curved sides. the sides of a polygon are also called its edges. the points where two sides meet are the vertices (or corners) of a polygon.

Here are some examples of polygons.

here are some examples of a polygon

polygon graph

Polygons are named by the number of sides they have. polygons are usually denoted by n-gon where n represents the number of sides it has, for example, a five-sided polygon is called a 5-gon, a ten-sided one is called a 10-gon, and so on.

However, few polygons have special names. the minimum number of sides a polygon can have is 3 because it needs a minimum of 3 sides to be a closed shape or else it will be open.

Although polygons with sides greater than 10 also have special names, we usually denote them with n-gon since the names are complex and not easy to remember.

polygon types

Polygons can be classified based on the number of sides and angles they have:

  1. classification according to sides: regular and irregular polygons:
  2. regular polygons: Polygons that have equal sides and equal angles are regular polygons.

    For example, an equilateral triangle is a regular polygon with three sides. A square is a regular polygon with four sides. a regular hexagon is a regular polygon with six sides.

    here are some examples of regular polygons.

    irregular polygons – polygons with unequal sides and angles are irregular polygons.

    here are some examples of irregular polygons.

    1. classification based on angles: convex and concave polygons:
    2. convex polygons: A convex polygon is a polygon with all interior angles less than 180°.

      in convex polygons, all diagonals are inside the polygon.

      (diagonal is a line segment joining two non-consecutive vertices of a polygon)

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      here are some examples of convex polygons.

      Concave polygons: A concave polygon is a polygon with at least one interior angle greater than 180°.

      in concave polygons, not all diagonals are inside the polygon.

      here are some examples of concave polygons.

      difference between convex and concave polygon

      3. simple and complex polygon:

      simple polygon: A simple polygon has only one boundary. the sides of a simple polygon do not intersect.

      complex polygon: complex polygon is a polygon whose sides intersect one or more times.

      sum of the angles of a polygon

      1. sum of the interior angles of a polygon:

      sum of the interior angles of a polygon with n sides = (n – 2) × 180°

      for example: consider the following 6-sided polygon

      here, ∠a + ∠b + ∠c + ∠d + ∠e + ∠f = (6 – 2) × 180° = 720° (n = 6 since the polygon has 6 sides)

      2. sum of the exterior angles of the polygons

      sum of the exterior angles of the polygons = 360°

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      the sum will always equal 360 degrees, regardless of how many sides it has.

      for example: consider the following 5-sided polygon

      here, ∠m + ∠n + ∠o + ∠p + ∠q = 360°

      angles in regular polygons

      in a regular polygon, all its

      • sides are equal
      • interior angles are equal
      • exterior angles are equal
      • interior angle:

        sum of the interior angles of a polygon with n sides = (n – 2) × 180°

        so, each interior angle = (n – 2) × 180n

        exterior angle:

        sum of the exterior angles of the polygons = 360°

        so, each exterior angle = 360°n

        sum of interior angle and exterior angle:

        whether the polygon is regular or irregular, at each vertex of the polygon the sum of one interior angle and one exterior angle is 180°.

        solved examples on polygon

        example 1: fill in the blank.

        1. the name of the three-sided regular polygon is ________________.
        2. A regular polygon is a polygon whose _____________ are equal and all angles are equal.
        3. The sum of the exterior angles of a polygon is __________.
        4. A polygon is a simple closed figure made up of only _______________.
        5. solution:

          1. equilateral triangle
          2. sides
          3. 360°
          4. line segments
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            Example 2: Write the number of sides of a given polygon.

            1. nonagon
            2. triangle
            3. pentagon
            4. decagon
            5. solution:

              1. 9
              2. 3
              3. 5
              4. 10
              5. Example 3: Find the measure of each exterior angle of a regular 20-sided polygon.

                solution:

                the polygon has 20 sides. so, n = 20.

                sum of the exterior angles of the polygons = 360°

                so, each exterior angle = 360°n = 360°20 = 18°

                example 4: the sum of the interior angles of a polygon is 1620°. How many sides does it have?

                solution:

                sum of the interior angles of a polygon with n sides = (n – 2) × 180°

                1620° = (n – 2) × 180°

                n – 2 = 1620180

                n – 2 = 9

                n = 9 + 2

                n = 11

                so, the given polygon has 11 sides.

                practice problems

                ffrequently asked questions

Content Creator Zaid Butt joined Silsala-e-Azeemia in 2004 as student of spirituality. Mr. Zahid Butt is an IT professional, his expertise include “Web/Graphic Designer, GUI, Visualizer and Web Developer” PH: +92-3217244554

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