How to Calculate Perimeter

Calculating the perimeter of a shape involves adding up the lengths of all its sides. The perimeter is the total distance around the outside of a shape, and it’s an important concept in geometry. Let’s explore how to calculate the perimeter for different shapes in detail.

1. Perimeter of a Rectangle

A rectangle has two pairs of equal sides. To calculate the perimeter, we add up the lengths of all four sides.

Formula:

Perimeter=2×(Length+Width)

Example:

Imagine a rectangle with a length of 8 units and a width of 5 units.

1. Identify the lengths of the sides:
   • Length = 8 units
   • Width = 5 units
2. Apply the formula: Perimeter=2×(8+5)=26 units

So, the perimeter of the rectangle is 26 units.

Diagram:

Here’s a simple diagram to visualize it:

+-----------------+
|                 |
|                 |
|                 |  Length = 8 units
|                 |
|                 |
+-----------------+
     Width = 5 units

2. Perimeter of a Square

A square has four equal sides. To calculate the perimeter, we multiply the length of one side by 4.

Formula:

Perimeter=4×Side length

Example:

Consider a square with each side measuring 6 units.

1. Identify the length of one side:
   • Side length = 6 units
2. Apply the formula: Perimeter=4×6=24 units

So, the perimeter of the square is 24 units.

Diagram:

Here’s how it looks:

+-------+
|       |
|       |
|       |  Side = 6 units
|       |
|       |
+-------+

3. Perimeter of a Triangle

The perimeter of a triangle is the sum of the lengths of its three sides.

Formula:

Perimeter = Side A + Side B + Side C

Example:

Let’s take a triangle with sides measuring 3 units, 4 units, and 5 units.

1. Identify the lengths of the sides:
   • Side A = 3 units
   • Side B = 4 units
   • Side C = 5 units
2. Apply the formula: Perimeter=3+4+5=12 units

So, the perimeter of the triangle is 12 units.

Diagram:

Here’s a simple illustration:

     /\
    /  \
3  /    \ 4
  /______\
     5

4. Perimeter of a Regular Polygon

A regular polygon has all sides of equal length. The perimeter is calculated by multiplying the length of one side by the total number of sides.

Formula:

Perimeter=Side length × Number of sides

Example:

Consider a regular hexagon (6 sides) with each side measuring 7 units.

1. Identify the length of one side:
   • Side length = 7 units
   • Number of sides = 6
2. Apply the formula: Perimeter=7×6=42 units

So, the perimeter of the hexagon is 42 units.

Diagram:

Imagine the hexagon:

    _______
  /         \
 /           \
 \           /
  \_________/

5. Perimeter of a Circle (Circumference)

The perimeter of a circle is called the circumference, and it’s calculated differently from polygons.

Formula:

Circumference=2×π×Radius

or

Circumference=π×Diameter

Where:

• π (Pi) is approximately 3.14159
• Radius is the distance from the center to the edge of the circle
• Diameter is twice the radius

Example:

Consider a circle with a radius of 3 units.

1. Identify the radius:
   • Radius = 3 units
2. Apply the formula: Circumference=2×3.14 x 3 = Circumference≈18.85 units

So, the circumference of the circle is approximately 18.85 units.

Diagram:

Here’s a simple circle:

      ______
     /      \
    |        |  Radius = 3 units
     \______/

Summary:

• Rectangle: Add all four sides or use 2×(Length+Width).
• Square: Multiply one side by 4.
• Triangle: Add all three sides.
• Regular Polygon: Multiply one side by the number of sides.
• Circle (Circumference): Use 2×π×Radius or π×Diameter.