## octagon

### An octagon is a geometric shape that consists of eight sides and eight angles

An octagon is a geometric shape that consists of eight sides and eight angles. It is a polygon, which means it is a closed figure with straight sides. All the sides of an octagon are equal in length and all the angles measure 135 degrees.

To better understand an octagon, let’s break down its characteristics:

1. Sides: An octagon has eight straight sides. All the sides are of equal length, meaning they are congruent to each other. For example, if one side of an octagon measures 5 units, then all the sides will also measure 5 units.

2. Angles: An octagon has eight angles, and all of them are equal in measure. Each angle of an octagon measures 135 degrees. The sum of all the internal angles in an octagon is 1080 degrees (180 degrees per triangle of the interior).

3. Diagonals: The diagonals of an octagon are line segments that connect any two non-adjacent vertices (corners) of the octagon. An octagon has a total of 20 diagonals. The formula to calculate the number of diagonals in an octagon is (n * (n – 3)) / 2, where n is the number of sides.

4. Symmetry: An octagon exhibits rotational symmetry of order 8. This means that the octagon can be rotated by any multiple of 45 degrees and it will appear the same as the original position.

In real-life, we can find many examples of octagons. Stop signs, for example, are often octagonal in shape. Some architectural structures like gazebos or even certain tiles and floors may be designed as octagons.

When working with an octagon in math problems, you may need to calculate properties such as perimeter and area. To find the perimeter, you add up the lengths of all the sides. And to find the area, you can use different formulas depending on the given information, such as the length of the sides or the apothem (the perpendicular distance from the center to one of the sides).

Remember that practice is key to becoming comfortable with any geometric shape, including the octagon. So, try solving different problems involving octagons to reinforce your understanding of their properties and calculations.

##### More Answers:

Exploring the Fundamentals and Applications of Geometry | Shapes, Sizes, and Relationships in the Three-Dimensional SpaceThe Importance of Sides in Mathematics | Exploring Geometric Shapes and Beyond

Understanding the Concept of Vertices | Exploring Mathematics, Geometry, and Graph Theory