Everything You Need to Know About Octagons | Sides, Angles, Vertices, and More

Octagon

An octagon is a polygon with eight sides, eight angles, and eight vertices

An octagon is a polygon with eight sides, eight angles, and eight vertices. The word “octagon” is derived from the Latin word “octo” which means eight. Each side of an octagon is of equal length, and each angle measures 135 degrees.

To better understand the properties of an octagon, let’s break it down further:

Sides: An octagon has eight sides. Since all sides are of equal length, an octagon is considered a regular polygon.

Angles: An octagon has eight interior angles and eight exterior angles. The interior angles of an octagon sum up to 1080 degrees, meaning each interior angle measures 135 degrees. The exterior angles of an octagon sum up to 360 degrees, so each exterior angle measures 45 degrees.

Vertices: An octagon has eight vertices, which are the meeting points of the sides.

Diagonals: A diagonal is a line segment connecting two non-adjacent vertices of a polygon. An octagon has a total of 20 diagonals, where each diagonal connects two vertices not next to each other.

Symmetry: An octagon has rotational symmetry of order 8, meaning there are eight distinct positions that can be reached through rotation by a certain angle. It also has bilateral symmetry, which means it can be divided into two equal halves through a line called a line of symmetry.

Area and Perimeter: To calculate the area of an octagon, you can divide it into eight isosceles triangles by drawing diagonals from each vertex to the center of the octagon. The formula to find the area of an octagon is A = 2(1 + √2) * s^2, where s represents the length of one side.

The perimeter of an octagon is the sum of all its side lengths. If the length of one side is s, then the perimeter is given by P = 8s.

Usage: Octagons are commonly found in architecture, design, and various other areas where a symmetrical shape with eight equal sides and angles is desired. For example, stop signs are octagonal in shape.

In summary, an octagon is a polygon with eight sides, eight angles, and eight vertices. It exhibits various symmetrical properties and has formulas for calculating its area and perimeter.

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