Hard

Perimeter and Area — Hard

15 questions 18 min PYQ-grade reasoning

Q1. Read the assertion and reason. Assertion (A): The perimeter of a rectangle of length 6 cm and breadth 4 cm is 20 cm. Reason (R): Perimeter of a rectangle = 2 × length × breadth. Which of the following is correct?
- A. Both A and R are true, and R is the correct explanation of A.
- B. Both A and R are true, but R is NOT the correct explanation of A.
- C. A is true, R is false.
- D. A is false, R is true.
Q2. A rectangular park is 150 m long and 120 m wide. What is the cost of fencing it once around at ₹40 per metre?
- A. ₹10,800
- B. ₹21,600
- C. ₹54,000
- D. ₹7,20,000
Q3. A farmer has a rectangular field 230 m long and 160 m wide. He wants to fence it with 3 rounds of rope. What total length of rope does he need?
- A. 780 m
- B. 1,170 m
- C. 2,340 m
- D. 1,10,400 m
Q4. On a dot grid, a right-angled triangle has two straight sides of 3 units each and a slant side along the diagonal. Akshi says the perimeter is 9 units. Toshi says it is more than 9 units. Who is correct?
- A. Toshi — the diagonal side is longer than a straight unit, so the perimeter is more than 6 + 3 = 9 units
- B. Akshi — the diagonal side equals one straight unit, so 3 + 3 + 3 = 9 units
- C. Both are correct because the perimeter can be either
- D. Neither — the perimeter is less than 9 units
Q5. Two rectangular tracks share a common centre. Akshi runs 5 rounds of the outer track (70 m × 40 m). Toshi runs 7 rounds of the inner track (60 m × 30 m). Who runs the longer total distance?
- A. Akshi — total 1,100 m vs Toshi's 900 m
- B. Toshi — total 1,260 m vs Akshi's 1,100 m
- C. Both run the same distance — 1,200 m each
- D. Akshi — total 1,400 m vs Toshi's 1,200 m
Q6. Three statements on why area uses squares not circles: I. Squares pack together without gaps. II. Circles cannot be packed tightly without gaps. III. The same rectangle gives the same count of circles every time it is packed. Which are correct?
- A. I and II only
- B. II and III only
- C. I and III only
- D. All three
Q7. The area of a rectangular garden is 300 sq m and its length is 25 m. What is its width?
- A. 100 m
- B. 275 m
- C. 275 sq m
- D. 12 m
Q8. Consider three rules used to estimate area on grid paper. I. Count one full small square as 1 sq unit. II. Count a square more than half-covered as 1 sq unit. III. Count a square less than half-covered as 1 sq unit too. Which rules are correct?
- A. I and II only
- B. II and III only
- C. I and II only — and III is the wrong rule
- D. All three
Q9. Read the assertion and reason. Assertion (A): A diagonal of a rectangle divides it into two triangles of equal area. Reason (R): The two triangles formed by a diagonal can be placed exactly on top of each other. Which of the following is correct?
- A. Both A and R are true, and R is the correct explanation of A.
- B. Both A and R are true, but R is NOT the correct explanation of A.
- C. A is true, R is false.
- D. A is false, R is true.
Q10. In the chapter, a blue triangle BAD (half of rectangle ABCD) and a red triangle ABE (with vertex E on side DC) look very different, yet have the same area. Which idea best explains this?
- A. Two triangles of equal area must always have the same shape.
- B. Triangle ABE is twice the area of triangle BAD because it looks bigger.
- C. Triangle ABE equals half the rectangle ABCD by splitting it into halves of two smaller rectangles — so its area equals that of BAD.
- D. Triangle ABE has no relation to rectangle ABCD.
Q11. In Charan's house plan, the Master Bedroom is 15 ft × 15 ft (area 225 sq ft), the Kitchen is 15 ft × 12 ft (180 sq ft) and the Small Bedroom has length 15 ft and area 180 sq ft. What is the breadth of the Small Bedroom?
- A. 10 ft
- B. 12 ft
- C. 15 ft
- D. 180 ft
Q12. In an area-maze puzzle, two side-by-side rectangles share the same width. The left rectangle has area 40 sq cm and the right rectangle has area 20 sq cm. The right rectangle is 5 cm long. What is the length of the left rectangle?
- A. 5 cm
- B. 8 cm
- C. 10 cm
- D. 20 cm
Q13. Consider three statements about closed figures. I. Two figures with the same area always have the same perimeter. II. Two figures with the same area can have different perimeters. III. Two figures with the same perimeter can have different areas. Which are correct?
- A. II and III only
- B. I and II only
- C. I and III only
- D. All three
Q14. Using 9 unit squares joined edge-to-edge (no holes), the LARGEST possible perimeter of the resulting figure is
- A. 12 units
- B. 20 units
- C. 18 units
- D. 36 units
Q15. What is the cost of tiling a rectangular plot 500 m long and 200 m wide at the rate of ₹8 per 100 sq m?
- A. ₹8,000
- B. ₹80,000
- C. ₹800
- D. ₹800,000

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