A 36-sided polygon, also known as a triacontakaihexagon, is a regular polygon with thirty-six equal sides and thirty-six equal angles. This geometric shape has a center point from which all vertices are equidistant, forming a nearly circular appearance due to its many sides.
A regular 36-sided polygon has several important mathematical properties. Each interior angle measures 170 degrees, while each exterior angle is 10 degrees. The sum of all interior angles equals 6120 degrees. Additionally, this polygon has 630 diagonals connecting non-adjacent vertices.
To understand the 36-sided polygon better, let's compare it with other regular polygons. Starting with a triangle having 3 sides, then a square with 4 sides, a hexagon with 6 sides, and a dodecagon with 12 sides. As we increase the number of sides, the polygon becomes more circular. The 36-sided polygon is very close to a perfect circle.
The mathematical properties of a 36-sided polygon can be calculated using specific formulas. The interior angle formula gives us 170 degrees for each angle. The area depends on the radius and uses trigonometric functions. The perimeter is simply the number of sides times the side length, and the number of diagonals is calculated using the combination formula.