# The Number of Sides in a Decagon

A decagon is a polygon with 10 sides, 10 vertices, and 10 angles. The word “decagon” comes from the Greek word “deka,” meaning ten, and “gonia,” meaning angle. Decagons are frequently used in geometry and architecture, and they have a range of interesting properties that make them a fascinating subject of study.

The sides of a decagon are all equal in length, and the internal angles of a decagon add up to 1440 degrees. Each internal angle measures 144 degrees, and each external angle measures 36 degrees. This means that the sum of the internal angles of any polygon of n sides is given by the formula (n-2)x180 degrees.

We can also calculate the area of a regular decagon using the formula A = (5/4) x s^2 x tan(π/10), where s is the length of each side. This formula can be derived using trigonometry, and it results in the area of the decagon being equal to approximately 7.6942 times the square of its side length.

The perimeter of a regular decagon can also be calculated using the formula P = 10s, where s is the length of each side. This means that if we know the length of one side of a regular decagon, we can easily calculate its perimeter.

Interestingly, decagons also have a range of interesting properties related to their symmetry. For example, a regular decagon has rotational symmetry of order 10, which means that it looks the same after being rotated by an angle of 36 degrees around its center point. It also has reflectional symmetry across its five lines of symmetry, which are the lines that bisect each pair of opposite vertices.

Decagons are frequently used in architecture, especially in the design of buildings and monuments. One notable example is the Library of Celsus in Ephesus, Turkey, which features a decagonal rotunda in its main hall. Another example is the Washington Monument in Washington D.C., which has a base that is shaped like a decagon.

In conclusion, the number of sides in a decagon is 10, and this polygon has a range of interesting properties related to its symmetry, angle measures, and area. Decagons are frequently used in geometry and architecture, and they provide a fascinating subject of study for math enthusiasts of all ages.