## polygon

### A polygon is a 2-dimensional geometric shape that is made up of straight lines connected end to end

A polygon is a 2-dimensional geometric shape that is made up of straight lines connected end to end. It is a closed figure with any number of sides greater than 2. The sides of a polygon do not cross each other.

Polygons can vary in shape and the number of sides they have. Some common polygons include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), heptagons (7 sides), octagons (8 sides), nonagons (9 sides), and decagons (10 sides). However, there are many other polygons that can exist based on the number of sides.

In addition to the number of sides, polygons are also classified based on their angles. There are two types of polygons: regular and irregular.

1. Regular Polygon: In a regular polygon, all the sides have the same length, and all the angles have the same measure. For example, a regular hexagon has six sides of equal length and six interior angles of equal measure.

2. Irregular Polygon: In an irregular polygon, the sides may have different lengths, and the angles may have different measures. The irregular polygon does not follow a specific pattern or rule for its sides and angles.

To find various properties of polygons, you can use different formulas:

1. Perimeter: The perimeter of a polygon is the total length of its sides. To find the perimeter, you add up the lengths of all the sides. For irregular polygons, you would measure the length of each side and add them together.

2. Area: The area of a polygon is the amount of space enclosed by its sides. The formula to find the area of various polygons depends on the type of polygon. For example, to find the area of a triangle, you can use the formula A = 1/2 * base * height. For regular polygons, there are different formulas available.

3. Interior Angles: The sum of the interior angles of a polygon can be found using the formula (n-2) * 180 degrees, where n represents the number of sides. For example, a quadrilateral (4 sides) has interior angles summing up to (4-2) * 180 = 360 degrees.

4. Exterior Angles: The exterior angle of a polygon is the angle formed between one side and the extension of an adjacent side. The sum of the exterior angles of any polygon is always 360 degrees.

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