## polygon

### A polygon is a closed two-dimensional shape with straight sides

A polygon is a closed two-dimensional shape with straight sides. It is formed by connecting line segments, also known as sides, that intersect only at their endpoints, known as vertices. The word “polygon” is derived from the Greek words “poly,” meaning many, and “gonia,” meaning angles.

There are various types of polygons, including triangles, quadrilaterals, pentagons, hexagons, and so on, depending on the number of sides they have. Each side of a polygon is a line segment, and each vertex is a point where two neighboring sides intersect. The angles formed at the vertices of a polygon are known as interior angles.

The sum of the interior angles of a polygon depends on the number of sides it has. For example, in a triangle, the sum of the interior angles is always 180 degrees. In a quadrilateral, the sum of the interior angles is 360 degrees. The formula to find the sum of the interior angles of a polygon with n sides is given by:

Sum of interior angles = (n – 2) * 180 degrees

Polygons can be classified based on their characteristics. Regular polygons have equal side lengths and equal interior angles. Irregular polygons have sides and angles that are not equal. Convex polygons are those in which no interior angles are greater than 180 degrees, whereas concave polygons have at least one interior angle greater than 180 degrees.

Polygons play a crucial role in various areas of mathematics, such as geometry and trigonometry. They are used to solve problems related to shape properties, area, perimeter, and angles.

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