The Complete Guide to Decagons | Properties, Formulas, and Real-Life Examples

decagon

A decagon is a polygon with ten sides and ten angles

A decagon is a polygon with ten sides and ten angles. It is formed by connecting ten straight line segments, or sides, to create a closed shape. Each side of a decagon is of equal length, and each angle measures 144 degrees.

The word “decagon” comes from the Greek words “deka,” meaning “ten,” and “gonia,” meaning “angle.” It is a regular polygon because all of its sides and angles are congruent (equal).

Properties of a Decagon:

1. Number of Sides: A decagon has ten sides.
2. Number of Angles: A decagon has ten angles.
3. Side Length: All sides of a regular decagon have the same length.
4. Angle Measure: Each angle in a regular decagon measures 144 degrees.
5. Sum of the Interior Angles: The sum of the interior angles of a decagon is equal to 1440 degrees.
(Formula: Sum of interior angles = (n – 2) * 180, where n is the number of sides)
6. Exterior Angles: Each exterior angle of a decagon measures 36 degrees.
(Formula: Exterior angle measure = 360 / n, where n is the number of sides)
7. Diagonals: A decagon has a total of 35 diagonals, which are line segments connecting non-adjacent vertices.
(Formula: Number of diagonals = n * (n – 3) / 2, where n is the number of sides)

It is worth noting that a decagon can be classified as regular or irregular. If all sides and angles are equal, it is a regular decagon. If the side lengths or angle measures vary, it is an irregular decagon.

Real-life examples of decagons can be found in various fields, including architecture, art, and design. For instance, a common shape used in traffic signs is a decagon, such as a stop sign, which has ten sides and angles.

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