This MCQ module is based on: 6.1 Perimeter
TOPIC 20 OF 41
6.1 Perimeter
🎓 Class 6
Mathematics
CBSE
Theory
Ch 6 — Perimeter and Area
⏱ ~15 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: 6.1 Perimeter
Targeting Class 6 level in Mensuration, with Basic difficulty.
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6.1 Perimeter
Do you remember what the perimeter? of a closed plane figure is? Imagine an ant walking around the outline of a shape — the total distance it covers is the perimeter.
Definition
The perimeter of any closed plane figure is the total distance covered along its boundary when you go around it once. For a polygon? (a closed figure made of straight line segments), the perimeter is simply the sum of the lengths of all its sides.
Perimeter of a Rectangle
Consider a rectangle ABCD with length 12 cm and breadth 8 cm. Its perimeter is the sum of all four sides:
Rectangle ABCD with length 12 cm and breadth 8 cm.
Perimeter = AB + BC + CD + DA = 12 + 8 + 12 + 8 = 40 cm.
Because opposite sides of a rectangle are equal (AB = CD and AD = BC), we can shortcut:
\(\text{Perimeter of a rectangle} = 2 \times (\text{length} + \text{breadth})\)
Perimeter of a Square
Debojeet wants to paste coloured tape around a square photo-frame of side 1 m. All four sides are equal, so:
\(\text{Perimeter of a square} = 4 \times \text{side}\)
Square frame of side 1 m — perimeter = 4 × 1 m = 4 m.
So Debojeet needs \(4 \times 1 = 4\,\text{m}\) of tape.
Perimeter of a Triangle
Consider a triangle with sides 5 cm, 7 cm and 4 cm. The perimeter is simply the sum of the three sides:
Triangle with sides 5, 4 and 7 cm. Perimeter = 5 + 7 + 4 = 16 cm.
Example — Akshi's Lace
Akshi wants to stitch lace around a rectangular tablecloth 3 m long and 2 m wide. How much lace does she need?
Perimeter = 2 × (3 + 2) = 10 m.
Example — Usha's Running
Usha walks around a square park of side 75 m, three times. Find the total distance covered.
Perimeter = 4 × 75 = 300 m. Three rounds = 3 × 300 = 900 m.
Figure it Out (Section 6.1)
Q1. Find the missing terms:
(a) Perimeter of rectangle = 14 cm, breadth = 2 cm, length = ?
(b) Perimeter of square = 20 cm, side = ?
(c) Perimeter of rectangle = 12 m, length = 3 m, breadth = ?
(a) Perimeter of rectangle = 14 cm, breadth = 2 cm, length = ?
(b) Perimeter of square = 20 cm, side = ?
(c) Perimeter of rectangle = 12 m, length = 3 m, breadth = ?
(a) \(2(L+2) = 14 \Rightarrow L = 5\) cm.
(b) side = 20/4 = 5 cm.
(c) \(2(3+B) = 12 \Rightarrow B = 3\) m.
(b) side = 20/4 = 5 cm.
(c) \(2(3+B) = 12 \Rightarrow B = 3\) m.
Q2. A rectangle has sides 5 cm and 3 cm — if straightened and bent into a square, what will the side of the square be?
Perimeter of rectangle = 2(5+3) = 16 cm. Square side = 16/4 = 4 cm.
Q3. Find the length of the third side of a triangle having perimeter 55 cm, and the other two sides 20 cm and 14 cm.
Third side = 55 − (20+14) = 21 cm.
Q4. What would be the cost of fencing a rectangular park of length 150 m and breadth 120 m, if the fence costs ₹40 per metre?
Perimeter = 2(150+120) = 540 m. Cost = 540 × 40 = ₹21,600.
Q5. A string of 36 m is cut into five pieces of equal length. What is the length of each, if used to form (a) a square, (b) an equilateral triangle, (c) a regular hexagon?
(a) 36/4 = 9 m per side. (b) 36/3 = 12 m per side. (c) 36/6 = 6 m per side.
Q6. A farmer has a rectangular field of length 230 m and breadth 160 m. He wants to fence it with 3 rounds of rope. What is the total length of rope needed?
Perimeter = 2(230+160) = 780 m. Three rounds = 3 × 780 = 2340 m.
Matha Pachchi! — The Running Puzzle
Akshi and Toshi race around two rectangular tracks. Akshi's track: 70 m × 40 m. Toshi's track (inside): 60 m × 30 m. Akshi completes 5 rounds; Toshi completes 7 rounds. Who ran the longer distance?
Two concentric running tracks. Akshi runs the outer, Toshi the inner.
Akshi's round = 2(70+40) = 220 m. Five rounds = 5 × 220 = 1100 m.
Toshi's round = 2(60+30) = 180 m. Seven rounds = 7 × 180 = 1260 m.
Toshi ran longer by 160 m!
🔵 Mark positions after specific distances — Q3 of section 6.1 Figure it Out. Using Akshi's perimeter 220 m, after 250 m Akshi will be 30 m beyond her first lap, i.e. at 30 m from start along the first side. Similar reasoning applies for other positions.
Activity: Measure the School Ground
L3 Apply
Materials: Measuring tape (or a 1 m string), notebook
Predict: Estimate the perimeter of your school ground in metres. Write your guess.
- Walk along each side of the ground, measuring with the tape.
- Record the lengths of all sides.
- Add them up to find the perimeter.
- Compare with your prediction — how close were you?
- Extension: if the fence costs ₹120 per metre, how much will a one-round fence cost?
Most school grounds are rectangular. Perimeter = 2(L + B). For a 50 m × 30 m ground, P = 160 m; cost at ₹120/m = ₹19,200.
Competency-Based Questions
Scenario: A gardener plans a rectangular flower-bed of length 15 m and breadth 9 m. He wants to plant saplings at equal intervals of 1.5 m along the boundary, and also fence the bed with wire.
Q1. How many metres of wire are needed for a single fence round?
L3 ApplyPerimeter = 2(15 + 9) = 48 m.
Q2. How many saplings will fit along the boundary if spaced 1.5 m apart?
L4 AnalyseNumber = 48 / 1.5 = 32 saplings.
Q3. If the gardener increases each dimension by 50%, evaluate by what factor the perimeter grows.
L5 EvaluateNew sides: 22.5 m and 13.5 m. New perimeter = 2(22.5+13.5) = 72 m. Factor = 72/48 = 1.5. Perimeter scales with the same factor as the sides.
Q4. Redesign the flower-bed as a square with the SAME perimeter of 48 m. What side will it have, and is the new area greater or less than the rectangle's?
L6 CreateSquare side = 48/4 = 12 m. Area = 144 m². Rectangle area = 15 × 9 = 135 m². Square area is greater. For a fixed perimeter, a square encloses more area than any other rectangle.
Assertion–Reason Questions
A: The perimeter of a square with side \(s\) is always \(4s\).
R: A square has four equal sides.
R: A square has four equal sides.
Answer: (a).
A: Two rectangles with the same area must have the same perimeter.
R: Perimeter is an additive quantity while area is multiplicative.
R: Perimeter is an additive quantity while area is multiplicative.
Answer: (d). A is false — e.g. a 2×6 rectangle (area 12, P=16) and a 3×4 rectangle (area 12, P=14). R is true.
Frequently Asked Questions — Perimeter and Area
What is Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool in NCERT Class 6 Mathematics?
Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool is a key concept covered in NCERT Class 6 Mathematics, Chapter 6: Perimeter and Area. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool step by step?
To solve problems on Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 6 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 6: Perimeter and Area?
The essential formulas of Chapter 6 (Perimeter and Area) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool important for the Class 6 board exam?
Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool is part of the NCERT Class 6 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool?
Common mistakes in Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool?
End-of-chapter NCERT exercises for Part 1 — Perimeter of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 6, and solve at least one previous-year board paper to consolidate your understanding.
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