Perimeter and Area Class 7 Worksheet — Free PDF Download with Answers

Mensuration questions are where students learn that maths lives inside the physical world. The floor of a classroom has an area. The fence around a garden has a length. The biscuit packet has a surface. A good worksheet gives students the chance to practise calculating these things in dozens of variations, until the formulas become automatic.

Here is what I see time and again with Class 7 students who only practise on apps. They can apply a formula when it is handed to them in a clean box. They cannot find the formula when they need to choose between rectangle and triangle, or when the figure is made up of two shapes joined together. Worksheets, with their written problems and varied figures, train this decision making muscle.

Writing by hand also helps with the one weakness exam markers comment on most — missing units. Students who tap their way through digital practice often forget to write cm or square metres on the final answer. On paper, with the habit of writing units at every step, the mistake is caught early.

There is also the question of diagram reading. A worksheet has printed figures that students must measure, label and calculate from. This skill transfers directly to exams, where the figure is usually rough and the student has to pull out the relevant measurements.

Finally, the break from screens matters. Mensuration is a good excuse for a 30 minute session with a pencil, a ruler and a printed sheet. It is one of those chapters where paper practice genuinely beats every alternative.

The worksheet covers every sub topic from the Class 7 Perimeter and Area chapter.

Sub topics:

* Perimeter of rectangle, square, triangle
* Area of rectangle, square, parallelogram
* Area of triangle
* Circumference and area of a circle
* Area of composite figures
* Conversion of units

Level breakdown:

Total 60 questions. Types include direct numerical, word problems and labelled diagram questions. Full answer key is provided.

Revise these formulas before starting.

* Perimeter of rectangle — $P = 2(l + b)$ where $l$ is length and $b$ is breadth.
* Area of rectangle — $A = l \times b$.
* Perimeter of square — $P = 4s$ where $s$ is the side.
* Area of square — $A = s^2$.
* Area of triangle — $A = \dfrac{1}{2} \times \text{base} \times \text{height}$.
* Area of parallelogram — $A = \text{base} \times \text{height}$.
* Circumference of circle — $C = 2\pi r$ where $r$ is the radius.
* Area of circle — $A = \pi r^2$.
* Value of pi — Use $\pi = \dfrac{22}{7}$ or $3.14$ as specified in the question.
* Unit conversions — $1\text{ m}^2 = 10000\text{ cm}^2$, $1\text{ km}^2 = 1000000\text{ m}^2$.

Quick tip: For composite figures, split the shape into simpler parts like rectangles and triangles. Find the area of each part separately, then add or subtract as needed.

Level 1 — Easy

1. Find the area of a rectangle with length $8$ cm and breadth $5$ cm.
Solution: $A = 8 \times 5 = 40$ cm$^2$.

2. Find the perimeter of a square of side $7$ cm.
Solution: $P = 4 \times 7 = 28$ cm.

3. Find the area of a triangle with base $10$ cm and height $6$ cm.
Solution: $A = \dfrac{1}{2} \times 10 \times 6 = 30$ cm$^2$.

Level 2 — Medium

1. Find the circumference of a circle with radius $14$ cm. Use $\pi = \dfrac{22}{7}$.
Solution: $C = 2 \times \dfrac{22}{7} \times 14 = 88$ cm.

2. A parallelogram has base $12$ cm and height $5$ cm. Find its area.
Solution: $A = 12 \times 5 = 60$ cm$^2$.

3. Find the area of a circle with radius $7$ m. Use $\pi = \dfrac{22}{7}$.
Solution: $A = \dfrac{22}{7} \times 7 \times 7 = 154$ m$^2$.

Level 3 — Hard

1. A room is $6$ m long and $4$ m wide. Find the cost of painting the floor at Rs. 50 per square metre.
Solution: Area $= 6 \times 4 = 24$ m$^2$. Cost $= 24 \times 50 = 1200$ rupees.

2. A rectangular park is $50$ m long and $30$ m wide. A path of width $2$ m runs along the inside boundary. Find the area of the path.
Solution: Outer area $= 50 \times 30 = 1500$ m$^2$. Inner dimensions $= 46 \times 26 = 1196$ m$^2$. Path area $= 1500 - 1196 = 304$ m$^2$.

3. A circular garden has a radius of $14$ m. Find the cost of fencing it at Rs. 25 per metre.
Solution: Circumference $= 2 \times \dfrac{22}{7} \times 14 = 88$ m. Cost $= 88 \times 25 = 2200$ rupees.

1. Print — Use plain A4 paper and a ruler.
2. Warm up — Write out all formulas from memory.
3. Time yourself — 20 minutes for Level 1, 30 for Level 2, 40 for Level 3.
4. Check answers — Use the answer key.
5. Revise mistakes — Redraw the diagram and solve again for every wrong answer.
6. Try again — Retry wrong questions next day.

Daily plan: 25 minutes per day for two weeks.

Weekly revision: Every weekend, measure a real object at home (like a book, a cushion, a room) and calculate its area or perimeter using the correct formula. This connects maths to life.

1. Missing units — Writing the answer as just $40$ instead of $40$ cm$^2$. Markers deduct marks for missing units.

2. Wrong power in units — Writing cm instead of cm$^2$ for area. Area is always in square units.

3. Mixing up radius and diameter — If the question gives the diameter, divide by $2$ to get the radius before using the formula.

4. Forgetting the half in triangle area — Writing $A = b \times h$ instead of $A = \dfrac{1}{2} b h$.

5. Pi value confusion — Using $\dfrac{22}{7}$ when the question says $3.14$. Always read the given value of pi carefully.

6. Wrong unit conversion — Converting $5$ m$^2$ to cm$^2$ as $500$ cm$^2$ instead of the correct $50000$ cm$^2$. Area conversions need squared factors.

CBSE (NCERT)
Perimeter and Area is Chapter 11 of NCERT Class 7 maths. Weightage is around 12 to 15 marks. Questions include basic formulas, circles and composite figures.

ICSE (Selina / ML Aggarwal)
ICSE calls the chapter Area and Perimeter. Weightage is around 15 marks. ICSE tends to include more complex composite figures and cost based word problems.

IB MYP
IB MYP treats area and perimeter as part of geometric measurement. Students measure real objects, calculate, and compare results across units. Emphasis is on modelling real world situations.

Download the free Class 7 Perimeter and Area worksheet:

* Area and Perimeter ICSE Worksheet
* Area and Perimeter IB Worksheet

Online practice:

* Area and Perimeter Online — ICSE
* Area and Perimeter Online — IB

* AI Maths Solver — Snap a photo of any mensuration problem for a step by step solution.
* Spark Coach — AI tutor for guided learning.
* Class 7 Maths Complete Guide
* All Worksheets Hub
* Class 7 Formulas

Week 1: Rectangles, squares and triangles

* Day 1: Read the chapter and make a formula card.
* Day 2: Level 1 questions 1 to 10.
* Day 3: Level 1 questions 11 to 20.
* Day 4: Level 2 triangle and parallelogram questions.
* Day 5: Level 2 circle questions.
* Day 6: Redo wrong answers.
* Day 7: Rest.

Week 2: Composites and word problems

* Day 8: Level 3 composite figure questions.
* Day 9: Level 3 word problems.
* Day 10: Redo wrong Level 3 answers.
* Day 11: Measure three real objects and calculate their area.
* Day 12: Mixed quiz.
* Day 13: Mock test (45 minutes).
* Day 14: Review.

* Class 7 Triangles Worksheet
* Class 7 Visualising Solid Shapes Worksheet
* Class 7 Symmetry Worksheet
* Class 7 Lines and Angles Worksheet
* Class 7 Maths Complete Guide