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Ask a Class 6 student for the perimeter of a 6 cm by 4 cm rectangle and you will often hear "24". That is its area. Perimeter and area use the same two measurements, so they are easy to mix up. This post explains what NCERT's new Class 6 chapter teaches, works through problems from the book and beyond, and gives a short routine for keeping the two ideas apart.
What does the Class 6 perimeter and area chapter cover?
Chapter 6 of Ganita Prakash, NCERT's Class 6 mathematics book (first edition August 2024, Reprint 2026-27), has three sections: perimeter, area and the area of a triangle. Its summary sets out the core results:
The perimeter of a polygon is the sum of the lengths of all its sides.
Perimeter of a rectangle = 2 × (length + breadth).
Perimeter of a square = 4 × side.
Area is the measure of the region a closed figure encloses, measured in square units.
Area of a rectangle = length × breadth; area of a square = side × side.
Two figures can have the same area but different perimeters, or the same perimeter but different areas.
What is the difference between perimeter and area?
Perimeter is a length. It answers "how far around?" and is measured in cm or m. Think of lace around a tablecloth or a fence around a park.
Area is a surface. It answers "how much space inside?" and is measured in square units such as sq cm or sq m. Think of a carpet covering a floor.
Worked example 1 (from the book). A rectangular park is 150 m long and 120 m wide, and fencing costs ₹40 per metre.
Perimeter = 2 × (150 + 120) = 2 × 270 = 540 m
Cost = 540 × 40 = ₹21,600
Fencing goes around the edge, so this is a perimeter question.
Worked example 2 (from the book). A floor is 5 m by 4 m, and a square carpet of side 3 m is laid on it. How much floor is not carpeted?
Floor area = 5 × 4 = 20 sq m
Carpet area = 3 × 3 = 9 sq m
Uncovered area = 20 − 9 = 11 sq m
Covering a surface is an area question.
Can two shapes have the same perimeter but different areas?
Yes, and the chapter wants you to see it with your own examples.
Worked example 3. You have a 16 cm piece of wire and bend it into rectangles with whole-number sides. Length + breadth must be 8 cm each time.
7 cm × 1 cm: area 7 sq cm
6 cm × 2 cm: area 12 sq cm
5 cm × 3 cm: area 15 sq cm
4 cm × 4 cm: area 16 sq cm
The perimeter stays 16 cm, but the area changes from 7 to 16 sq cm. The square encloses the most. The book has a related problem: a 5 cm by 3 cm rectangle of wire, straightened and bent into a square, gives a square of side 16 ÷ 4 = 4 cm.
Worked example 4. Now keep the area at 12 sq cm and change the shape.
12 × 1: perimeter 2 × 13 = 26 cm
6 × 2: perimeter 2 × 8 = 16 cm
4 × 3: perimeter 2 × 7 = 14 cm
Same area, three different perimeters.
How do you handle problems with rounds and tracks?
The chapter has Akshi running 5 rounds of an outer track 70 m by 40 m, while Toshi runs 7 rounds of an inner track whose perimeter, given in the book's answers, is 180 m.
Akshi: one round = 2 × (70 + 40) = 220 m; five rounds = 5 × 220 = 1100 m
Toshi: seven rounds = 7 × 180 = 1260 m
Toshi runs farther, even though her track is shorter, because she runs more rounds. Multi-step questions like this reward writing each step on its own line.
Why do students mix up the two formulas?
They are not alone. In a test of 445 sixth-grade students in Ankara, Tan Sisman and Aksu (2016) found a wide range of misconceptions in length, area and volume, including "confusing area formula with perimeter formula". They read these errors as signs that students had learned formulas without understanding the ideas behind them and how they relate.
The fix is to tie each formula to a picture. Perimeter is walking around the edge and adding sides. Area is counting unit squares inside, which the book recalls from squared-paper work in earlier grades.
Which mistakes cost the most marks?
Swapping the formulas. Picture the fence or the carpet first.
Wrong units. Perimeter in cm; area in sq cm.
Mixing units. Convert first: 1 m = 100 cm, so 1 sq m = 100 × 100 = 10,000 sq cm.
Adding only two sides. A rectangle's perimeter has all four sides, which is why the formula doubles length + breadth.
Assuming same perimeter means same area. Worked example 3 shows it does not.
How should you practise this week?
Day 1: Measure your table and a notebook; find each perimeter and area.
Day 2: Draw every whole-number rectangle with perimeter 20 cm and list their areas.
Day 3: Draw every whole-number rectangle with area 24 sq cm and list their perimeters.
Day 4: Solve three mixed word problems, writing "around" or "inside" before you start each.
Day 5: Estimate the area of your hand on squared paper by counting squares.
If shapes make more sense when you can see them change, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read. You will build on these ideas with trapeziums and polygons in Class 8; see our post on area in Class 8.
Tonight, measure one room at home and work out both its perimeter and its floor area, with the right unit for each.
