medium difficulty5 min

Perimeter of Polygons

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

In one line: Perimeter means the path around the figure.

Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1Find the perimeter of a triangle with sides 8 cm, 10 cm, and 12 cm.
2Perimeter = 8 + 10 + 12 = 30 cm.

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

Common wrong answer

For a 12 cm by 7 cm rectangle, 19 cm.

Why it loses marks: It adds only length and breadth once.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

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

1
Enough for 1 mark
The perimeter of a polygon is the total length of all its sides.
2
Add for 2 marks
Example: A rectangle of length 12 cm and breadth 7 cm has perimeter 2(12 + 7) = 38 cm.
3
Add for 3 marks
For any closed figure made of straight sides, walk once around the boundary and add every side length.

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