Perimeter - Definition, Unit, Formula and Examples

Perimeter

Perimeter is one of the most fundamental concepts in geometry. It represents the total length around the boundary of a two-dimensional shape. Understanding perimeter is essential in daily life, from measuring the edges of a garden to designing frames or calculating fencing requirements. It helps us determine how much material is needed to enclose or outline a particular space.

In mathematical terms, perimeter is measured in linear units such as centimeters, meters, or feet. It applies to both regular shapes, where all sides are equal, and irregular shapes, where sides have different lengths.Students will learn more about perimeter, how to find it for different shapes, its units, common formulas, real-world examples, and the difference between perimeter and area and more below.

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What is Perimeter?

The definition of perimeter in geometry is:

Perimeter is the total distance around the boundary of a two-dimensional shape.

In simple terms, if you walk all the way around the edges of a shape, the total distance you cover is its perimeter.

It is found by adding the lengths of all sides of the figure. The perimeter helps determine the boundary length required for enclosing or outlining any flat shape, such as squares, rectangles, triangles, or circles (where the perimeter is called the circumference).

Key Points:

• The perimeter is a linear measurement, meaning it measures length only.

• It helps in finding the total boundary of any shape.

• It applies to both regular shapes (equal sides) and irregular shapes (unequal sides).

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How to Find Perimeter of Shapes?

To find the perimeter of any two-dimensional shape, the total length of its outer boundary must be measured. The perimeter depends on the shape’s structure and the number of its sides. Each shape has its own formula to calculate the perimeter accurately. Below are the main perimeter formulas for common geometric shapes.

Perimeter of a Square

A square has four equal sides.

The perimeter of a square is calculated by multiplying one side by four.

Formula: Perimeter = 4 × side

This formula works for all squares, as each side has the same length.

Perimeter of a Rectangle

A rectangle has opposite sides that are equal in length.

The perimeter of a rectangle is found by adding the lengths of all sides or by using the formula below.

Formula: Perimeter = 2 × (Length + Breadth)

This gives the total distance around the rectangle.

Perimeter of a Triangle

A  Preimeter of triangle has three sides, and its perimeter is the total of all three side lengths.

Formula: Perimeter = a + b + c

This formula applies to all types of triangles, whether scalene, isosceles, or equilateral.

Perimeter of a Circle (Circumference)

In perimeter of a circle, the boundary length is called the circumference, which acts as the perimeter of the shape.

Formula: Perimeter (Circumference) = 2πr

Here, r represents the radius, and π (pi) is approximately 3.1416.

Perimeter of a Regular Polygon

A regular polygon has equal sides and equal angles. The perimeter of a regular polygon is calculated by multiplying the number of sides by the length of one side.

Formula: Perimeter = Number of sides × Side length

This formula applies to regular shapes like pentagons, hexagons, and octagons.

Perimeter of an Irregular Polygon

An irregular polygon has sides of different lengths. To find its perimeter, measure each side separately and add all the side lengths together.

Formula: Perimeter = Sum of all sides

This method applies to shapes without equal sides or symmetry.

Perimeter of a Parallelogram

A parallelogram has opposite sides equal and parallel. The perimeter is calculated by adding twice the length and twice the breadth.

Formula: Perimeter = 2 × (Length + Breadth)

This formula also applies to special types of parallelograms such as rectangles and rhombuses.

Read More - Area of Isosceles Triangle - Formula, Definition, Examples

Perimeter of a Rhombus

Perimeter of a rhombus has four sides of equal length. Therefore, its perimeter can be calculated by multiplying one side by four.

Formula: Perimeter = 4 × side

Although similar to the formula for a square, a rhombus does not require equal angles.

Perimeter of a Trapezium (Trapezoid)

A trapezium has four sides, with one pair of sides parallel to each other. The perimeter is obtained by adding the lengths of all four sides.

Formula: Perimeter = a + b + c + d

This gives the total boundary length of the trapezium.

Perimeter of an Ellipse

An ellipse is an oval-shaped figure, and its perimeter is slightly more complex to calculate. The approximate formula to find the perimeter of an ellipse is:

Formula (Approximate): Perimeter = 2π √((a² + b²)/2)

Here, a and b represent the semi-major and semi-minor axes of the ellipse.

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Perimeter Units

Perimeter units are always linear because the perimeter measures length, not area or volume. The units depend on the measuring system used (metric or imperial).

Common Units:

• Millimeters (mm)

• Centimeters (cm)

• Meters (m)

• Kilometers (km)

• Inches (in)

• Feet (ft)

• Yards (yd)

Conversion Examples:

• 1 m = 100 cm

• 1 ft = 12 in

• 1 km = 1000 m

• 1 yd = 3 ft

Perimeter Formula 

The perimeter formula varies depending on the shape. Below are the most common formulas used in geometry.

Examples of Perimeter

Let’s look at some perimeter examples to understand the concept clearly.

Example 1: Square

• Side = 6 cm

• Perimeter = 4 × 6 = 24 cm

Example 2: Rectangle

• Length = 8 cm, Breadth = 3 cm

• Perimeter = 2 × (8 + 3) = 22 cm

Example 3: Triangle

• Sides = 5 cm, 6 cm, 7 cm

• Perimeter = 5 + 6 + 7 = 18 cm

Example 4: Circle

• Radius = 7 cm

• Perimeter (Circumference) = 2πr = 2 × 3.1416 × 7 ≈ 43.98 cm

Example 5: Regular Pentagon

• Each side = 4 cm

• Perimeter = 5 × 4 = 20 cm

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Difference Between Perimeter and Area

Understanding the difference between perimeter and area is very important in geometry. Though both terms are used in measuring shapes, they describe different aspects.

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