Chapter 13 of 14
Chapter 13: Fields and Fences
Perimeter of Irregular Polygons, Wire Fencing Calculations & Grid Square Area Counting | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Perimeter is the total continuous length of the outer boundary of a closed planar shape.
- Calculating perimeter by adding lengths of all straight boundary edges.
- Fencing fields with wire: single round vs. multiple rounds (e.g., 3-wire barbed fence).
- Counting whole and half squares on a square centimetre grid to estimate surface area.
All Textbook Exercises & In-Text Tasks (15 Questions)
100% Complete Ingestion
Q1
Boundary Length & Wire Requirement
Rahmat is a farmer. He has a field with sides measuring 9 m, 15 m, 21 m, and 9 m. (a) What is the length of the boundary of Rahmat's field? (b) Rahmat bought a roll of 70 metres of barbed wire to fence his field. How much wire will be left over after putting one complete round of fence?
[3 Marks]
✅ Step-by-Step Solution & Working
(a) Length of boundary (Perimeter):
Sum of all sides = 9 m + 15 m + 21 m + 9 m = 54 metres.
(b) Wire remaining:
• Total wire in roll = 70 metres.
• Wire used for 1 round = 54 metres.
• Wire left over = 70 m - 54 m = 16 metres.
Sum of all sides = 9 m + 15 m + 21 m + 9 m = 54 metres.
(b) Wire remaining:
• Total wire in roll = 70 metres.
• Wire used for 1 round = 54 metres.
• Wire left over = 70 m - 54 m = 16 metres.
CBSE Step-by-Step Marking Scheme
Correct boundary sum 54 metres
1.5 M
Correct remaining wire 16 metres
1.5 M
Q2
Square Grid Area & Perimeter
A square has a side of 6 cm. (a) What is its perimeter? (b) If four 1 cm squares are cut out from its four corners, what is the perimeter of the new shape? Explain why the perimeter changes or stays the same.
[3 Marks]
✅ Step-by-Step Solution & Working
(a) Perimeter of original square:
Perimeter = 4 × side = 4 × 6 cm = 24 cm.
(b) Perimeter after cutting 1 cm squares from each corner:
• When a 1 cm square is removed from a corner, the two outer 1 cm edges that are removed are replaced by two inner 1 cm edges that form the new stepped corner.
• Therefore, the total boundary length remains exactly 24 cm!
• Conclusion: The perimeter stays the same (24 cm), even though the area has decreased by 4 sq cm.
Perimeter = 4 × side = 4 × 6 cm = 24 cm.
(b) Perimeter after cutting 1 cm squares from each corner:
• When a 1 cm square is removed from a corner, the two outer 1 cm edges that are removed are replaced by two inner 1 cm edges that form the new stepped corner.
• Therefore, the total boundary length remains exactly 24 cm!
• Conclusion: The perimeter stays the same (24 cm), even though the area has decreased by 4 sq cm.
CBSE Step-by-Step Marking Scheme
Original perimeter 24 cm
1.0 M
Explains corner cut effect and confirms perimeter remains 24 cm
2.0 M
Q3
Area & Perimeter • Grid Squares
A shape is drawn on a 1 cm square grid. It covers 12 complete squares and 6 half squares. (a) What is the area of this shape in square centimetres? (b) If each square has side 1 cm, what is the area of 1 unit square?
[3 Marks]
✅ Step-by-Step Solution & Working
Grid Area Calculation:
• Area of 1 unit square with side 1 cm = 1 cm × 1 cm = 1 sq cm.
1. 12 complete squares = 12 × 1 sq cm = 12 sq cm.
2. 6 half squares = 6 × (1/2 sq cm) = 3 sq cm.
Total Area of the Shape:
12 + 3 = 15 sq cm.
• Area of 1 unit square with side 1 cm = 1 cm × 1 cm = 1 sq cm.
1. 12 complete squares = 12 × 1 sq cm = 12 sq cm.
2. 6 half squares = 6 × (1/2 sq cm) = 3 sq cm.
Total Area of the Shape:
12 + 3 = 15 sq cm.
CBSE Step-by-Step Marking Scheme
Area of 1 unit square = 1 sq cm
1.0 M
Combining complete and half squares accurately (12 + 3)
1.0 M
Total area: 15 sq cm
1.0 M
Q4
Field Fencing • Barbed Wire Math
Ganpat has a field with sides 15 m, 20 m, 18 m, and 27 m. He bought a 100-metre roll of barbed wire to fence the boundary once. (a) What is the perimeter of his field? (b) How much wire will be left over after fencing?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Perimeter of the Field:
Perimeter = Sum of all 4 sides
= 15 m + 20 m + 18 m + 27 m = 80 metres.
2. Wire Left Over:
Wire roll length = 100 m
Wire used = 80 m
Leftover wire = 100 m - 80 m = 20 metres.
1. Perimeter of the Field:
Perimeter = Sum of all 4 sides
= 15 m + 20 m + 18 m + 27 m = 80 metres.
2. Wire Left Over:
Wire roll length = 100 m
Wire used = 80 m
Leftover wire = 100 m - 80 m = 20 metres.
CBSE Step-by-Step Marking Scheme
Correct sum of sides = 80 m
1.5 M
Subtraction 100 - 80 = 20 m left
1.5 M
Q5
Building with Bricks • Brick Geometry & Measurement
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?
[3 Marks]
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long?
✅ Step-by-Step Solution & Working
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
A Trip to Bhopal • Diesel Fuel Budget
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?
[3 Marks]
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay?
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
Long and Short • Height Comparisons
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?
[2 Marks]
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)?
✅ Step-by-Step Solution & Working
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
Tick-Tick-Tick • Expiry Dates on Food
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
[2 Marks]
✅ Step-by-Step Solution & Working
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
The Junk Seller • Loan and Interest
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?
[3 Marks]
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank?
✅ Step-by-Step Solution & Working
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
Jugs and Mugs • Measuring Medicine Dose
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?
[3 Marks]
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last?
✅ Step-by-Step Solution & Working
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
Carts and Wheels • Circle Geometry
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?
[2 Marks]
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle?
✅ Step-by-Step Solution & Working
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Halves and Quarters • Fraction Sharing
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?
[3 Marks]
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left?
✅ Step-by-Step Solution & Working
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
Play with Patterns • Secret Message Cipher
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?
[2 Marks]
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell?
✅ Step-by-Step Solution & Working
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
Tables and Shares • Division with Remainder
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over?
[2 Marks]
(a) How many complete bouquets can she make?
(b) How many roses will be left over?
✅ Step-by-Step Solution & Working
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
Review Questions • True or False
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.
[3 Marks]
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time.
✅ Step-by-Step Solution & Working
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study
Three-Strand Wire Fence Budget
A farmer wants to put a 3-strand barbed wire fence around a rectangular field that is 40 metres long and 25 metres wide. Fencing wire costs ₹15 per metre.
Analytical Task: Calculate the total length of wire needed and the total cost.
Evaluation & Model Answer:
Step 1: Perimeter:
2 × (40 + 25) = 2 × 65 = 130 metres.
Step 2: 3 strands:
130 m × 3 = 390 metres of wire.
Step 3: Total cost:
390 m × ₹15/m = ₹5,850.
2 × (40 + 25) = 2 × 65 = 130 metres.
Step 2: 3 strands:
130 m × 3 = 390 metres of wire.
Step 3: Total cost:
390 m × ₹15/m = ₹5,850.
Rubric: 1 Mark for perimeter (130 m); 1 Mark for 3 strands (390 m); 1 Mark for ₹5,850.