Octagon

An octagon refers to a polygon in geometry having 8 sides and 8 angles. Thus, as it has got 8 sides and angles, the vertices and the number of edges will also be 8. All these sides join together with one another in order to create a shape. All the sides of an octagon are in a straight-line form. In other words, they are not curved or disjoint with each other. Moreover, every interior angle of a regular polygon will be 135° so the measure of the exterior angle will be 180° – 135° which is 45°. Similarly, the sum of the interior angles of an octagon will be 135 × 8 which is 1080°.

Polygons

Looking at the above figure we see that an octagon comprises 8 sides and eight vertices. This makes it a regular octagon as the angles and sides are all equal. Similarly, we have other kinds of polygons that divide on the basis of the sides and angles. They are triangles, quadrilaterals, pentagons, hexagons, septagons, nonagons, decagons, and more.

Shape

An octagon is a geometrical shape which is a two-dimensional plane. Just like the other polygon shapes that you study in geometry like triangle, square, hexagon, rectangle and more, the octagon also comes under the category of a polygon. It is different from the other geometrical shapes because of its 8 sides and 8 angles.

Types of Octagon

On the basis of the sides and angles of the octagon, we can classify them in categories of regular and irregular then concave and convex. A regular one is when all the sides are equal and angles as well. On the other hand, an irregular one is which has unequal sides and unequal angles.

A regular one has a close shape having equal length sides and interior angles too having the same measurement. It consists of 8 symmetric lines plus a rotational equilibrium of order 8. Moreover, this one has an interior angle at each vertex of 135° and the central angle is 45°.

Further, there is a convex octagon that has all its angles which point outside or no angles which point inwards. Similarly, its angles aren’t more than 180°. On the other hand, the concave one is where one of its angles points inwards.

Properties

As we are taking a look at the properties of octagons, we will consider the regular ones for the same.

1. They comprise of 8 sides and 8 angles as well.
2. It comprises of equal sides and angles correspondingly.
3. A regular one consists of a total of 20 diagonals.
4. 1080° is the total sum of the interior angles. Over here, each angle is equal to 135°. The explanation is 135×8 = 1080.
5. Finally, 360° is the sum of all exterior angles of this one where each angle is equal to 45°. Meaning, 45×8=360.

Solved Questions for You

Question 1: How many sides does an octagon have?

Answer: Octagons are polygons that basically have eight sides, over here a polygon is a two-dimensional shape having straight sides. Moreover, vertices are the corners where the sides of this shape meet. Similarly, we see that no. of vertices of a polygon are closely linked to the no. of sides that a polygon has.

Question 2: Is an octagon a regular polygon?

Answer: No, it is not a regular polygon. A regular octagon is a regular polygon, but in general, it is not necessary for it to comprise uniform sides and angles. It is merely a polygon that has 8 sides.