Area and Perimeter - Perimeter of Regular and Irregular Polygons

Perimeter is the total length of the boundary or the outer edge of a closed geometric figure. Imagine walking around the edge of a park; the total distance covered in one full lap is the perimeter.

Units of perimeter are always linear, such as millimeters ($mm$), centimeters ($cm$), meters ($m$), or kilometers ($km$). If you were to 'unroll' the boundary of a shape into a straight line, its length would equal the perimeter.

A Regular Polygon is a flat shape where all sides are equal in length and all interior angles are equal. Visually, these shapes appear perfectly symmetrical, such as an equilateral triangle, a square, or a regular hexagon.

The perimeter of a Regular Polygon is calculated by multiplying the length of one side by the total number of sides ($n$). For example, a regular pentagon looks like a house shape with five equal sides, so its perimeter is $5 \times \text{side length}$.

An Irregular Polygon is a shape where sides and angles are not all the same. Visually, these shapes look 'stretched' or 'uneven,' like a scalene triangle or an L-shaped room. To find its perimeter, you must add the lengths of all its individual sides together.

A Rectangle is a common polygon where opposite sides are equal in length. Visually, it has a longer side called length ($l$) and a shorter side called width ($w$). Its perimeter is the sum of two lengths and two widths, often grouped as $2 \times (l + w)$.

A Square is a specific type of regular polygon with four equal sides and four right angles. Visually, it looks perfectly balanced. Because all four sides are identical, the perimeter is simply $4 \times s$.