Perimeter and Area — Mastery

Q1. For which of the following figures does "perimeter" make sense as defined in the chapter?

• A. A closed plane figure made up of line segments
• B. A single isolated point on a sheet of paper
• C. A straight line that extends without end in both directions
• D. An angle made by two rays from a common vertex

Q2. A square has side 5 cm. Which of the following is correct?

• A. Its perimeter is 25 cm and its area is 20 sq cm.
• B. Its perimeter is 25 sq cm and its area is 20 cm.
• C. Its perimeter is 10 cm and its area is 10 sq cm.
• D. Its perimeter is 20 cm and its area is 25 sq cm.

Q3. A rectangle has length 10 cm and breadth 4 cm. If only its length is doubled (breadth unchanged), what happens to its perimeter?

• A. Perimeter increases by 20 cm (from 28 cm to 48 cm).
• B. Perimeter doubles (from 28 cm to 56 cm).
• C. Perimeter stays the same.
• D. Perimeter increases by 10 cm (from 28 cm to 38 cm).

Q4. Why is the perimeter of a square written as 4 × side instead of (side + side + side + side)?

• A. Both expressions give the same result, and 4 × side is just a shorter way to write it
• B. 4 × side is the area of the square
• C. 4 × side gives a value four times larger than the actual perimeter
• D. Only (side + side + side + side) is correct in geometry

Q5. If the side of a square is tripled (made 3 times the original), what happens to its perimeter?

• A. It is doubled (becomes 2 times the original perimeter)
• B. It stays the same
• C. It becomes 9 times the original perimeter
• D. It is tripled (becomes 3 times the original perimeter)

Q6. For a scalene triangle (a triangle whose three sides all have different lengths), the perimeter must be found by

• A. Multiplying any one side by 3
• B. Doubling the longest side and adding the shortest
• C. Adding the lengths of all three sides
• D. Multiplying the three side lengths together

Q7. An isosceles triangle has two equal sides of 6 cm each and a third side of 8 cm. Its perimeter is

• A. 18 cm
• B. 14 cm
• C. 12 cm
• D. 20 cm

Q8. The perimeter of a regular pentagon (5 equal sides) is 35 cm. What is the length of one side?

• A. 5 cm
• B. 7 cm
• C. 9 cm
• D. 8.75 cm

Q9. The perimeter of a regular hexagon is 48 cm. What is the length of each side?

• A. 8 cm
• B. 12 cm
• C. 6 cm
• D. 16 cm

Q10. A rectangular vegetable plot is 9 m long and 6 m wide. Ravi wants to enclose it with two rounds of rope. What total length of rope does he need?

• A. 15 m
• B. 30 m
• C. 60 m
• D. 108 m

Q11. A teacher asks Priya to first estimate the perimeter of a random paper shape and then measure it with a scale. The best classroom purpose of "estimate, then measure" is to

• A. Show that estimation is always more accurate than measurement
• B. Replace the use of scales and measuring tapes
• C. Compare your estimate against the measured value to improve your sense of length
• D. Prove that perimeter has no fixed value

Q12. For which of these can we sensibly talk about "area" as defined in the chapter?

• A. A line segment of length 5 cm
• B. A single point on a sheet of paper
• C. A closed plane figure such as a rectangle
• D. A ray starting at one point

Q13. A rectangular garden is 50 m long and its area is 1000 sq m. What is its width?

• A. 10 m
• B. 15 m
• C. 20 m
• D. 25 m

Q14. A Class 6 student writes the area of a rectangle 5 m × 4 m as "20 m". Which of the following best describes the error?

• A. The arithmetic is wrong; the answer should be 9 m
• B. The unit is wrong — area must be expressed in square units (sq m), not in m
• C. The order of multiplication is wrong; it should be 4 × 5
• D. There is no error; "20 m" is correct for area

Q15. Four square flower beds, each of side 4 m, are placed at the four corners of a piece of land 12 m long and 10 m wide. What is the total area covered by the four flower beds?

• A. 16 sq m
• B. 32 sq m
• C. 48 sq m
• D. 64 sq m

Q16. The area of a square is 49 sq cm. What is the length of each side?

• A. 12.25 cm
• B. 24.5 cm
• C. 7 cm
• D. 14 cm

Q17. A student writes "area of a square of side 5 cm = 4 × 5 = 20 cm". Which of the following is the best correction?

• A. Area = 5 + 5 = 10 sq cm
• B. Area = 5 × 5 = 25 sq cm (the formula 4 × side is for perimeter, not area)
• C. Area = 4 × 5 = 20 sq cm (only the unit is wrong)
• D. Area = 2 × 5 = 10 cm (perimeter and area are the same here)

Q18. On graph paper, a leaf-shape covers 12 full unit squares, 6 squares that are more than half-covered, 4 squares that are exactly half-covered and 5 squares less than half-covered. What is its estimated area?

• A. 16 sq units
• B. 18 sq units
• C. 22 sq units
• D. 20 sq units

Q19. Two students estimate the area of the same irregular leaf-shape on graph paper. Priya counts 18 sq units and Ravi counts 19 sq units. Which statement is the best explanation?

• A. One of the two estimates must be exactly correct; the other is wrong
• B. Estimates of an irregular shape can differ slightly because the half-square rule is applied to boundary squares by judgement
• C. Both must always count exactly the same number of squares for the same shape
• D. Counting squares cannot be used for irregular shapes

Q20. A rectangle ABCD has length 8 cm and breadth 5 cm. A diagonal BD divides it into two triangles. What is the area of triangle BAD?

• A. 40 sq cm
• B. 20 sq cm
• C. 26 sq cm
• D. 13 sq cm

Q21. A rectangle is cut along one of its diagonals to make two triangles. Which of the following best describes the two triangles?

• A. They have the same area and can be placed exactly on top of each other after a flip
• B. They have different areas but the same perimeter
• C. They have the same perimeter but different areas
• D. They are similar in shape but the bigger one has twice the area

Q22. A triangle PQR sits inside a rectangle of length 10 cm and breadth 6 cm such that the triangle is exactly half of the rectangle. The area of the triangle PQR is

• A. 60 sq cm
• B. 20 sq cm
• C. 16 sq cm
• D. 30 sq cm

Q23. An L-shaped figure can be split into two rectangles, one of size 5 m × 3 m and another of size 4 m × 2 m. What is the area of the L-shaped figure?

• A. 20 sq m
• B. 23 sq m
• C. 14 sq m
• D. 26 sq m

Q24. A 6 cm × 4 cm paper rectangle is cut into two equal pieces and the pieces are rejoined to form a long thin rectangle 12 cm × 2 cm. Which statement is true?

• A. Area decreases; perimeter decreases
• B. Area decreases; perimeter increases
• C. Area stays the same; perimeter decreases
• D. Area stays the same; perimeter increases

Q25. Using 9 unit squares joined edge-to-edge with no holes, the SMALLEST possible perimeter of the resulting figure is

• A. 9 units
• B. 10 units
• C. 12 units
• D. 16 units

Q26. Different rectangles with whole-number sides each have area 24 sq units. Which pair has the GREATEST and the LEAST perimeter respectively?

• A. Greatest: 4 × 6 (perimeter 20); Least: 1 × 24 (perimeter 50)
• B. Greatest: 2 × 12 (perimeter 28); Least: 4 × 6 (perimeter 20)
• C. Greatest: 4 × 6 (perimeter 20); Least: 3 × 8 (perimeter 22)
• D. Greatest: 1 × 24 (perimeter 50); Least: 4 × 6 (perimeter 20)

Q27. Which of the following is true about the units sq cm and sq m?

• A. 1 sq m equals the area of a square of side 1 m, while 1 sq cm equals the area of a square of side 1 cm
• B. 1 sq m is equal to 100 sq cm
• C. 1 sq cm is larger than 1 sq m
• D. sq cm and sq m measure perimeter, not area

Q28. A Class 6 student insists, "If a figure has a bigger perimeter, it must have a bigger area." Which is the BEST teacher response to address this misconception?

• A. Simply tell the student the rule is wrong and move on to the next topic
• B. Show two figures with the same area but different perimeters — for example, two arrangements of 9 unit squares with perimeters 12 and 20 — and let the student see the counter-example
• C. Ask the student to memorise the formula 2 × (l + b) for perimeter
• D. Give the student more sums on calculating area until the idea goes away

Q29. A teacher is starting the area chapter with a Class 6 group that has never measured area before. Which of the following is the BEST first activity?

• A. Give the formula "area = length × width" and ask students to memorise it
• B. Solve five word problems on cost of tiling before introducing the concept
• C. Begin with the area of a triangle, then move to rectangles and squares
• D. Provide square grid paper and let students trace and count unit squares inside leaves, hand-drawn shapes and rectangles

Q30. A teacher gives Class 6 students 9 paper squares and asks them to first PREDICT how the perimeter will change as they rearrange the same 9 squares, then OBSERVE by counting, then EXPLAIN. The MAIN learning gain of this Predict–Observe–Explain (POE) sequence is that students

• A. Memorise the area of a square more quickly
• B. Learn to draw straight lines using a ruler
• C. Practise multiplication tables of 9
• D. Discover for themselves that area can stay the same while perimeter changes