Octagon is a polygon in geometry, which has 8 sides and 8 angles. That means the number of vertices is 8 and the number of edges is 8. All the sides are joint with each other end-to-end to form a shape. These sides are in a straight line form, they are not curved or disjoint with each other. Each interior angle of a regular polygon is 135°, therefore, the measure of exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of the octagon is 135 × 8 = 1080°.


Shape of Octagon

Octagon is a geometrical shape in a two-dimensional plane. Like the other polygon shapes, we have studied in geometry, such as triangle, square, pentagon, hexagon, rectangle, etc., the octagon is also a polygon. The points which define it different from other geometrical shapes is that it has 8 sides and 8 angles.

Types of Octagon

Depending upon the sides and angles of the octagon, it is classified into the following categories;

  • Regular and Irregular Octagon
  • Concave and Convex Octagon

Regular and Irregular Octagon

When an octagon has all equal sides and equal angles, then it is defined as regular octagon but with unequal sides and unequal angles, it is defined as an irregular octagon. See the figure below to see the difference between them.

Regular and Irregular Octagon

Convex and Concave Octagon

The octagon which has all its angles pointing outside or no angles are pointing inwards, is a convex octagon. The angles of the convex octagon are not more than 180°.

Convex and Concave Octagon

Properties of Octagon

In the case of properties, we usually consider regular octagons.

  • These have eight sides and eight angles.
  • All the sides and all the angles are equal respectively.
  • There is a total of 20 diagonals in a regular octagon.
  • The total sum of the interior angles is 1080°, where each angle is equal to 135°(135×8 = 1080)
  • Sum of all the exterior angles of the octagon is 360° and each angle is 45°(45×8=360).

Area of Octagon

Area of the octagon is the region covered by the sides of the octagon and its formula is given as;

Area = 2a2(1+√2)

To derive the formula for the area of the octagon, visit us here – Octagon Formula.

Perimeter of Octagon

The perimeter of the octagon is the length of the sides or boundaries of the octagon, which forms a closed shape.


Perimeter = Sum of all Sides = 8a

Where a is the length of one side of the octagon.

Octagon Example

Suppose the length of the side of a regular octagon is 5cm. Find its perimeter and area.

Solution: Given, a = 5cm

Therefore, Perimeter = 8a = 8 × 5 = 40cm

And Area = 2a2(1+√2) = 2 × 52 (1+√2) = 2 × 25 (1+√2)= 120.7 cm2

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