An octagon is a geometric shape that belongs to the family of polygons. It is specifically defined as a polygon with eight straight sides and eight vertices or corners. The word octagon comes from the Greek words octo meaning eight and gon meaning angle.
There are two main types of octagons. A regular octagon has all sides of equal length and all interior angles equal to one hundred thirty-five degrees. An irregular octagon has sides of different lengths and angles that may vary. The regular octagon is the most common and recognizable form.
A regular octagon has several important mathematical properties. Each interior angle measures exactly one hundred thirty-five degrees, and the sum of all interior angles is one thousand eighty degrees. The area formula involves the side length s and equals two times one plus square root of two times s squared. The perimeter is simply eight times the side length.
Octagons appear frequently in our daily lives. The most recognizable example is the traffic stop sign, which uses a regular octagon shape for high visibility and recognition. Octagons are also used in architecture for building designs, decorative floor tiles, and various patterns. In nature, some flowers have eight petals forming an octagonal shape.
To summarize what we have learned about octagons: An octagon is a polygon with eight sides and eight vertices. Regular octagons have all sides equal and interior angles of one hundred thirty-five degrees. We see octagons commonly in stop signs and architectural designs. Understanding octagons helps us recognize geometric patterns in both mathematics and the world around us.