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Formulas for Perimeter in Math

The Essential Guide to Calculating Boundaries

The perimeter is the total distance around the outside of a two-dimensional shape. Whether you are fencing a garden, framing a picture, or running around a track, you are dealing with perimeter.

In mathematics, "Perimeter" comes from the Greek words peri (around) and metron (measure). To calculate it, we generally add up the lengths of all the sides of the shape.

1. Perimeter of a Rectangle

A rectangle has four sides where opposite sides are equal in length. To find the perimeter, we add the length and width twice.

[Image of perimeter of a rectangle formula]
Formula: P = 2 × (Length + Width)

Example: If a rectangle has a length of 10m and a width of 5m:
P = 2 × (10 + 5) = 2 × 15 = 30m.

2. Perimeter of a Square

A square is a special type of rectangle where all four sides are equal. Instead of adding the sides individually, we can simply multiply the length of one side by 4.

Formula: P = 4 × Side

Example: If one side of a square is 6cm:
P = 4 × 6 = 24cm.

3. Perimeter of a Triangle

A triangle has three sides. The perimeter is simply the sum of the lengths of all three sides. The formula varies slightly depending on the type of triangle.

[Image of perimeter of a triangle]

General Triangle

Formula: P = a + b + c

Where a, b, and c are the lengths of the three sides.

Equilateral Triangle

Since all three sides are equal in an equilateral triangle:

Formula: P = 3 × Side

4. Perimeter of a Circle (Circumference)

The perimeter of a circle has a special name: Circumference. Because a circle has no straight sides, we use the constant Pi (π), which is approximately 3.14.

[Image of circumference of a circle formula]
Formula: C = 2 × π × r
OR
Formula: C = π × d
  • r = radius (distance from center to edge)
  • d = diameter (distance across the circle passing through the center)

5. Perimeter of Regular Polygons

A regular polygon is a shape where all sides are of equal length (like a pentagon or hexagon). The formula is straightforward:

Formula: P = n × s
  • n = number of sides
  • s = length of one side

Example: For a regular Hexagon (6 sides) with a side length of 4cm:
P = 6 × 4 = 24cm.

Conclusion

Understanding the formulas for perimeter is fundamental in geometry. By identifying the shape and applying the correct formula, you can easily calculate the boundary length of any object.