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Octagon - Shape, Types, Properties, Angle sum property, perimeter of an octagon and Area of Octagon

 

In geometry, a shape formed by joining straight lines is called a polygon. A polygon can have any number of sides, the smallest being a triangle which is a three-sided polygon. Polygons are geometric shapes named on the basis of a number of sides. For example,

  1. Triangle- a three-sided polygon
  2. Quadrilateral- a four-sided polygon. Examples: square, rectangle, parallelogram
  3. Pentagon- a five-sided polygon
  4. Hexagon- a six-sided polygon
  5. Heptagon- a seven-sided polygon
  6. Octagon- an eight-sided polygon

And so on, depending on the number of sides and interior angles. In Geometry circle is considered a polygon that has infinite sides.

Octagon

An octagon is an eight-sided closed polygon. It has eight vertices which make eight interior angles.

The above is an octagon sides AB, BC, CD, DE, EF, FG, GH and HA.

Types of octagons

Octagons can be classified on the basis of length of sides and angles as

  1. Regular octagon - A regular octagon is one that has all its sides equal. The length of the sides of a regular octagon is the same. The measure of each of its interior angles is 135°. This also means that each exterior angle corresponding to an interior angle in a regular heptagon is 45.
    Interior angle = 135°
    Exterior angle = 180° – interior angle
    Exterior angle = 180° – 135°
    Exterior angle = 45°
  2. Irregular octagon - An irregular octagon is one that has all its sides and angles different from each other. Sides are not equal in length, and angles are unequal in measurement.
  3. Convex octagon - An octagon which has all its angles directed outwards is called a convex octagon. All the angles in a convex octagon are less than 180°.
  4. Concave octagon - An octagon which has any of its angles directed inwards is called a concave octagon. The angles in a concave octagon are more than 180°.

Properties of an octagon

  1. For A regular Octagon, all the sides and angles are equal.
  2. An octagon can have 20 diagonals.
  3. The sum of its interior angles is equal to 1080° in a regular octagon.
  4. For a regular octagon, the sum of its exterior angles is 360°.

Angle sum property of a Octagon

The angle sum property of an octagon is the sum of all its interior angles. It can be calculated by the given formula.
(n – 2) . 180°
Angle sum property of an octagon = (8 – 2). 180°
Angle sum property of an octagon = 6 . 180°
Angle sum property of an octagon = 1080°
Where n is the number of sides.

The perimeter of an octagon

The perimeter of an octagon is the length of the boundary of an octagon. It can be calculated by adding all sides of a given octagon. For a regular octagon, the perimeter can be calculated by the formula.

Perimeter = 8 . length of side

For an irregular octagon, the perimeter is the sum of it’s sides.

Area of an octagon

The perimeter of a heptagon is the measure of the total boundary length of the heptagon. It is calculated by adding all the sides of the given heptagon. For a regular heptagon, the perimeter of the heptagon is obtained as the product of measure of one of its sides by 7.

Perimeter of a regular heptagon = 7 . length of a side

Area of Octagon

The area of an octagon can be obtained by the formula as below:

Area = 2(1 + √2) . side²

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