Class 6 Maths Chapter 6 Perimeter and Area Extra Questions

Rectangles, squares, and triangles are the shapes under scrutiny in this Chapter 6 question set, which applies the perimeter and area formulas to real numbers.

Last Updated: September 23, 2026

Very Short Answer Questions

Q1. What is the formula for the perimeter of a rectangle?
Answer: 2 × (length + breadth).

Q2. What is the formula for the area of a triangle?
Answer: ½ × base × height.

Q3. Find the perimeter of a square of side 7 cm.
Answer: 4 × 7 = 28 cm.

Q4. Find the area of a rectangle 9 m by 6 m.
Answer: 9 × 6 = 54 sq.m.

Q5. In what unit is area measured?
Answer: Square units (e.g., sq.cm, sq.m).

Short Answer Questions

Q6. A rectangular park is 80 m long and 50 m wide. Find the cost of fencing it at Rs.25 per metre.
Answer: Perimeter = 2(80+50) = 260 m. Cost = 260 × 25 = Rs.6,500.

Q7. Find the area of a triangle with base 10 cm and height 6 cm.
Answer: ½ × 10 × 6 = 30 sq.cm.

Q8. A square garden has a perimeter of 48 m. Find its area.
Answer: Side = 48 ÷ 4 = 12 m. Area = 12 × 12 = 144 sq.m.

Q9. A rectangle has an area of 72 sq.cm and breadth 8 cm. Find its length and perimeter.
Answer: Length = 72 ÷ 8 = 9 cm. Perimeter = 2(9+8) = 34 cm.

Q10. A rectangular hall is 40 m by 30 m. It is to be tiled at a cost of Rs.15 per sq.m. Find the total cost.
Answer: Area = 40 × 30 = 1,200 sq.m. Cost = 1,200 × 15 = Rs.18,000.

Long Answer / Reasoning Questions

Q11. Two rectangles have the same perimeter of 40 cm but different dimensions: one is 15 cm x 5 cm, the other is 10 cm x 10 cm. Compare their areas and explain the pattern.
Answer: First rectangle: area = 15 × 5 = 75 sq.cm. Second rectangle (a square): area = 10 × 10 = 100 sq.cm. Even with the same perimeter, the square-shaped rectangle has a greater area — this illustrates that among all rectangles with a fixed perimeter, the one closest to a square encloses the most area.

Q12. A farmer wants to fence a rectangular field with 100 m of wire, using whole-number side lengths, to enclose the maximum possible area. What dimensions should the farmer choose, and what is that maximum area?
Answer: With a fixed perimeter of 100 m, 2(l+b)=100, so l+b=50. To maximise area (l×b) with a fixed sum, the dimensions should be as close to equal as possible: l = b = 25 m (a square), giving maximum area = 25 × 25 = 625 sq.m.

Q13. A path of uniform width 2 m runs around the outside of a rectangular garden measuring 20 m by 15 m. Find the area of the path.
Answer: Outer dimensions including the path: (20+2+2) × (15+2+2) = 24 × 19 = 456 sq.m. Garden area = 20 × 15 = 300 sq.m. Path area = 456 − 300 = 156 sq.m.

Q14. An L-shaped room is formed by removing a 3 m × 2 m rectangular corner from a 10 m × 8 m rectangle. Find the area of the L-shaped room.
Answer: Full rectangle area = 10 × 8 = 80 sq.m. Removed corner area = 3 × 2 = 6 sq.m. L-shaped area = 80 − 6 = 74 sq.m.

Q15. Explain, with an example, why two shapes can have the same area but different perimeters.
Answer: Area measures the surface covered, while perimeter measures the boundary length — these depend on shape in different ways. For example, a 6 cm × 6 cm square has area 36 sq.cm and perimeter 24 cm, while a 12 cm × 3 cm rectangle also has area 36 sq.cm but perimeter 2(12+3)=30 cm. Both enclose the same surface area, but the more elongated shape has a longer boundary.

Practice more:

• Extra Questions for Class 6 Maths Chapter 1: Patterns in Mathematics
• Class 6 Maths Chapter 2 Lines and Angles Extra Questions
• Class 6 Maths Chapter 3 Number Play Extra Questions
• Class 6 Maths Chapter 4 Data Handling and Presentation Extra Questions
• Class 6 Maths Chapter 5 Prime Time Extra Questions

Frequently Asked Questions

If a rectangular garden is 8 metres long and 5 metres wide, how much fencing would be needed to enclose it, and what is its area?
The perimeter is 2 times the sum of length and width, giving 2 times 13 equals 26 metres, while the area is length multiplied by width, giving 8 times 5 equals 40 square metres.

Why might two rectangles with the same perimeter have different areas?
For a fixed perimeter, different combinations of length and width can be chosen, and since area depends on multiplying these dimensions, different combinations can result in noticeably different areas.

Written by Satish

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