Perimeter and Area Class 6 Worksheet — Free PDF Download with Answers

Perimeter is the total length of the boundary of a shape. Area is the amount of surface enclosed within that boundary. These are two of the most practical concepts in mathematics — you use them every time you fence a garden, tile a floor, or wrap a gift.

In Class 6, students work with the perimeter and area of basic shapes: squares, rectangles, and triangles. They also encounter composite shapes formed by combining these basic figures. The chapter builds on the measurement skills learned in earlier classes and prepares students for the more advanced mensuration topics (circles, 3D shapes) in Classes 7 and 8.

A common error at this level is confusing perimeter with area. Perimeter is measured in linear units (cm, m) while area is measured in square units (cm$^2$, m$^2$). This worksheet provides extensive practice to ensure students never mix the two.

Revise these formulas before starting:

* Perimeter of a rectangle — $P = 2(l + b)$, where $l$ = length and $b$ = breadth.
* Area of a rectangle — $A = l \times b$.
* Perimeter of a square — $P = 4s$, where $s$ = side.
* Area of a square — $A = s^2$.
* Perimeter of a triangle — $P = a + b + c$, where $a, b, c$ are the three sides.
* Area of a triangle — $A = \dfrac{1}{2} \times \text{base} \times \text{height}$.
* Unit conversions:
- $1 \text{ m} = 100 \text{ cm}$
- $1 \text{ m}^2 = 10{,}000 \text{ cm}^2$
- $1 \text{ km} = 1{,}000 \text{ m}$
* Composite shapes — Split the shape into rectangles/triangles, find each area separately, then add (or subtract for cutouts).
* Given perimeter, find side — Rearrange the formula. E.g., if $P = 2(l+b)$ and $P, l$ are known, then $b = \dfrac{P}{2} - l$.

1. Print the PDF — Download from the links below. Keep a ruler and pencil handy for drawing.

2. Start with Level 1 (Easy) — 20 questions on direct formula application for rectangles and squares.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the included answer key. Pay attention to units in your answers.

5. Revise mistakes — Redraw the figure, label all dimensions, and rework the problem from scratch.

6. Move to the next level — Progress when you score 16/20 or above.

Level 1 — Easy

1. Find the perimeter of a rectangle with length $12$ cm and breadth $8$ cm.
Solution: $P = 2(12 + 8) = 2 \times 20 = 40$ cm.

2. Find the area of a square with side $9$ cm.
Solution: $A = 9^2 = 81$ cm$^2$.

3. A triangle has sides $5$ cm, $7$ cm, and $10$ cm. Find its perimeter.
Solution: $P = 5 + 7 + 10 = 22$ cm.

Level 2 — Medium

1. The perimeter of a rectangle is $56$ cm and its length is $18$ cm. Find its breadth and area.
Solution: $b = \dfrac{56}{2} - 18 = 28 - 18 = 10$ cm. Area $= 18 \times 10 = 180$ cm$^2$.

2. A rectangular garden is $25$ m long and $15$ m wide. Find the cost of fencing it at Rs. $12$ per metre.
Solution: Perimeter $= 2(25 + 15) = 80$ m. Cost $= 80 \times 12 =$ Rs. $960$.

3. Find the area of a triangle with base $14$ cm and height $9$ cm.
Solution: $A = \dfrac{1}{2} \times 14 \times 9 = 63$ cm$^2$.

Level 3 — Hard

1. An L-shaped room consists of a $10 \text{ m} \times 8 \text{ m}$ rectangle with a $4 \text{ m} \times 3 \text{ m}$ rectangle cut from one corner. Find the area.
Solution: Area $= (10 \times 8) - (4 \times 3) = 80 - 12 = 68$ m$^2$.

2. The area of a square field is $2{,}500$ m$^2$. Find its perimeter in metres.
Solution: Side $= \sqrt{2500} = 50$ m. Perimeter $= 4 \times 50 = 200$ m.

3. A path $2$ m wide runs inside a rectangular park of dimensions $40 \text{ m} \times 30 \text{ m}$. Find the area of the path.
Solution: Inner dimensions $= (40 - 4) \times (30 - 4) = 36 \times 26 = 936$ m$^2$. Outer area $= 40 \times 30 = 1{,}200$ m$^2$. Path area $= 1{,}200 - 936 = 264$ m$^2$.

CBSE (NCERT — Ganita Prakash / Math Magic)
The "Perimeter and Area" chapter covers rectangles, squares, and introduces triangles. CBSE emphasises word problems involving fencing, flooring, and painting. The Ganita Prakash textbook adds hands-on activities like measuring the school playground.

ICSE (Selina / ML Aggarwal)
ICSE covers this under "Area and Perimeter" and includes more complex composite shapes and unit-conversion problems. ICSE exams often include cost-based word problems (cost of tiling, painting) and problems involving paths around or inside rectangles.

IB MYP (Mathematics Framework)
The MYP "Measurement & Units" unit focuses on understanding measurement as a concept. Students explore why area is measured in square units through investigation, and apply perimeter and area to real-world design tasks (e.g., planning a room layout).

Key Differences:
* CBSE: Formula-based with practical word problems.
* ICSE: Composite shapes and cost-based problems emphasised.
* IB: Investigative; understanding why formulas work.

Download your free Perimeter and Area worksheets:

* Perimeter and Area CBSE Worksheet — 60 questions aligned to NCERT
* Area & Perimeter ICSE Worksheet — 60 questions aligned to Selina / ML Aggarwal

Practise online:

* Practice Online — CBSE
* Practice Online — ICSE
* Practice Online — IB

Each worksheet has 20 questions per level with a detailed answer key.

* AI Maths Solver — Upload a diagram and get step-by-step area/perimeter solutions.
* Spark Coach — AI tutor that guides with hints, not answers.
* Free Worksheets for All Classes — Worksheets from Class 1 to 10 across all boards.
* Play Mode for Class 1-4 — Fun measurement games for younger learners.

Explore more Class 6 worksheets:

* Lines and Angles Class 6 Worksheet
* Constructions & Practical Geometry Class 6 Worksheet
* Symmetry Class 6 Worksheet
* Data Handling Class 6 Worksheet
* Fractions & Decimals Class 6 Worksheet