Subject: Geometry

# Polygon Angles

Angles in polygons tells so much about the nature of the polygon. With this information, we can get several important properties regarding polygons such as its area, perimeter and even volume. Knowledge of these properties are an important tool not just in mathematics and theoretical science but most importantly in engineering and science applications. In this article, we'll talk about sides in polygons with known angles to calculate a polygon's property such as its perimeter.

## Perimeter of a Polygon

Perimeter is defined as the total distance around the outside of an object. In this case, its the polygon. But the outside of the polygon is interconnected with its sides in the vertex, thus, the perimeter is also the sum of all sides of a polygon.

Perimeter = S_1 +S_2 + S_3 + \cdot \cdot \cdot + S_n

where n is the number of sides and S_n is the distance of side n.

Finding the perimeter of a polygon can be attributed to its interior angles. When a polygon has equal interior angles, it is called regular polygons and when its interior angles are not equal, then it is called irregular polygons. So what does this have to do with finding the polygon's perimeter? Well, its because regular polygons are easy to deal with when it comes to calculating its perimeters.

### Perimeter of a regular polygon

Since the interior angles of regular polygons are equal, then its sides are also equal. So instead of adding all sides one by one to find its perimeter, we can just multiply the length of one side to the number of sides a polygon has. Therefore, the perimeter P of a regular polygon is

P = n\cdot S

In the figure above, the perimeter of that polygon with 5 sides is P = 5\cdot 5 = 25 cm.

### Perimeter of an irregular polygon

Irregular polygons have irregular shapes and different interior angle values. That's why we can't make a "shortcut" formula to find its perimeter. It follows the same long procedure stated above by adding all sides manually.

P = S_1 +S_2 + S_3 + \cdot \cdot \cdot + S_n

So for the polygon below;

the perimeter will be calculated as P = 2 cm + 3 cm + 3.4 cm + 4.5 cm + 5 cm + 6 cm = 23.9 cm.

## Perimeter of Various Polygon Types

Frequently occurring polygons and its perimeter will be discussed briefly below.

### Triangle

Perimeter of a triangle is basically the sum of the triangle's three sides.

P = S_1 + S_2 + S_3

### Rectangle

A rectangle has four sides, whose two sides are equal. Then, its perimeter is;

P = x + x + y +y = 2 (x+y)

### Square

It has four equal sides. In fact, it is one of the regular polygons whose n = 4. Thus,

P = n\cdot S = 4\cdot S