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Perimeter of Polygons

The perimeter of a polygon is the total length of all its sides.

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Student-friendly explanation

For any closed figure made of straight sides, walk once around the boundary and add every side length. For regular polygons, all sides are equal, so multiplication saves time.

How to write this in exams

  1. 1

    Start with the exact idea

    The perimeter of a polygon is the total length of all its sides.

  2. 2

    Then show how to use it

    Identify all boundary sides, write their lengths in the same unit, add them once each, and write the answer with a length unit.

  3. 3

    Add one concrete example

    A rectangle of length 12 cm and breadth 7 cm has perimeter 2(12 + 7) = 38 cm.

  4. 4

    Avoid this incomplete answer

    For a 12 cm by 7 cm rectangle, 19 cm is wrong because it adds only length and breadth once.

Definition

The perimeter of a polygon is the total length of all its sides.

Example

A rectangle of length 12 cm and breadth 7 cm has perimeter 2(12 + 7) = 38 cm.

Rule to remember

Triangle: a + b + c; rectangle: 2(l + b); square: 4a; regular polygon: number of sides × side length.

Memory hook

Perimeter means the path around the figure.

Examples and method

Worked example

Find the perimeter of a triangle with sides 8 cm, 10 cm, and 12 cm. Perimeter = 8 + 10 + 12 = 30 cm.

Method to apply

Identify all boundary sides, write their lengths in the same unit, add them once each, and write the answer with a length unit.

Diagram support

A simple labelled polygon diagram can show each side length and the path around the boundary.

How CBSE asks it

Questions may give side lengths directly, give a regular polygon, or ask for a missing side when perimeter is known.

Avoid common mistakes

Common confusion

Students sometimes add only two sides of a rectangle, forgetting that opposite sides are also part of the boundary.

Common wrong answer

For a 12 cm by 7 cm rectangle, 19 cm is wrong because it adds only length and breadth once.

Exam tip

Always check whether the question asks for boundary length or surface area before choosing a formula.

Quick check

A regular hexagon has each side 5 cm. What is its perimeter?

The perimeter is 6 × 5 = 30 cm because a regular hexagon has six equal sides.

Answer writing and exam use

1-mark answer

The perimeter of a polygon is the total length of all its sides.

2-mark answer

The perimeter of a polygon is the total length of all its sides. Triangle: a + b + c; rectangle: 2(l + b); square: 4a; regular polygon: number of sides × side length. A rectangle of length 12 cm and breadth 7 cm has perimeter 2(12 + 7) = 38 cm.

3-mark answer

For any closed figure made of straight sides, walk once around the boundary and add every side length. For regular polygons, all sides are equal, so multiplication saves time. Triangle: a + b + c; rectangle: 2(l + b); square: 4a; regular polygon: number of sides × side length. Find the perimeter of a triangle with sides 8 cm, 10 cm, and 12 cm. Perimeter = 8 + 10 + 12 = 30 cm. Questions may give side lengths directly, give a regular polygon, or ask for a missing side when perimeter is known. For a 12 cm by 7 cm rectangle, 19 cm is wrong because it adds only length and breadth once.
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