CBSE Class 6 Mathematics Perimeter and Area MCQs Set 11

Answer: (b) the distance covered along its boundary in one complete round

Explanation:
1. Perimeter is the distance we travel when we go once all the way round the boundary of a closed figure.
2. The region enclosed inside the figure is its area, not its perimeter.
3. So the perimeter is the distance covered along its boundary in one complete round.

Teacher's Note:
1. Think of walking once round a park.
2. Boundary means perimeter; inside means area.

Answer: (c) the sum of the lengths of all its sides

Explanation:
1. A polygon is a closed figure made only of line segments.
2. Going once round it means travelling along every side once.
3. So the perimeter is the sum of the lengths of all its sides.

Teacher's Note:
1. 'Four times one side' works only for a square.
2. Add every side, one by one.

Answer: (d) 2 × (l + b)

Explanation:
1. Opposite sides of a rectangle are equal, so its sides are l, b, l and b.
2. Perimeter = l + b + l + b = 2 × (l + b).
3. l × b is the area, not the perimeter.

Teacher's Note:
1. A rectangle has two lengths and two breadths.
2. Do not mix up the perimeter and area formulas.

Answer: (b) square units such as sq cm and sq m

Explanation:
1. Area is found by counting how many unit squares cover a region.
2. So it is written in square units such as sq cm and sq m.
3. Metres and centimetres are units of length, used for perimeter.

Teacher's Note:
1. Area units always have the word 'square'.
2. Kilograms measure weight and litres measure volume.

Answer: (a) s × s

Explanation:
1. Area of a square = side × side.
2. With side s, the area is s × s.
3. 4 × s is the perimeter of the square, not its area.

Teacher's Note:
1. Area multiplies two sides; perimeter adds four sides.
2. 4 × s is a common trap.

Answer: (d) perimeter of the tablecloth

Explanation:
1. The lace runs along the edges, that is, along the boundary of the tablecloth.
2. The length of the boundary is the perimeter of the tablecloth.

Teacher's Note:
1. 'All around' is a clue word for perimeter.
2. Area would be needed only to cover the whole cloth.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A square has four sides, and R is true: all of them are equal.
2. So side + side + side + side = 4 × side, and A is true.
3. A follows directly from R, so R is the correct explanation of A.

Teacher's Note:
1. Adding four equal numbers is the same as multiplying by 4.
2. Ask: does R give the reason for A?

Answer: (c) A is true, but R is false.

Explanation:
1. Area is measured in square units, so writing it in sq cm is correct. A is true.
2. The distance all around the boundary is the perimeter, not the area. R is false.
3. So A is true but R is false.

Teacher's Note:
1. Check each statement separately first.
2. R describes perimeter, not area.

Answer: (a) Only Statement I is true

Explanation:
1. Statement I is the correct meaning of perimeter, so it is true.
2. Perimeter of the square = 4 × 5 = 20 cm, not 25 cm, so Statement II is false.
3. So only Statement I is true.

Teacher's Note:
1. 25 = 5 × 5 is the area in sq cm, not the perimeter.
2. Perimeter of a square = 4 × side.

Answer: (a) (i)-(p), (ii)-(q), (iii)-(s), (iv)-(r)

Explanation:
1. A square has 4 equal sides: 4 × side (p). A rectangle: 2 × (length + breadth) (q).
2. An equilateral triangle has 3 equal sides: 3 × side (s). A regular pentagon has 5 equal sides: 5 × side (r).
3. So the match is (i)-(p), (ii)-(q), (iii)-(s), (iv)-(r).

Teacher's Note:
1. For a regular figure, multiply the side by the number of sides.
2. Triangle means 3; pentagon means 5.

Answer: (c) 7 square units

Explanation:
1. The bottom row of the shaded shape has 4 full squares.
2. The row above it has 3 full squares.
3. Area = 4 + 3 = 7 square units.

Teacher's Note:
1. Count row by row so that no square is missed.
2. Every square here is full, so no halves are needed.

Answer: (b) 28 m

Explanation:
1. The fence goes along all six sides: 5 m, 2 m, 3 m, 4 m, 8 m and 6 m.
2. Length of fence = 5 + 2 + 3 + 4 + 8 + 6 = 28 m.
3. Check: the L has the same perimeter as an 8 m × 6 m rectangle, 2 × (8 + 6) = 28 m.

Teacher's Note:
1. Go round the figure in one direction and tick each side.
2. An L-shape has six sides, not four.

Answer: (d) 42 cm

Explanation:
1. A regular hexagon has 6 equal sides.
2. Perimeter = 6 × 7 = 42 cm.

Teacher's Note:
1. Hexa means six.
2. Number of sides × length of one side.

Answer: (b) Its area stays the same, but its perimeter may change.

Explanation:
1. No paper is added or thrown away, so the total area stays 24 sq cm.
2. But the edges that get hidden where the pieces meet can be of different lengths, so the perimeter can change.
3. So its area stays the same, but its perimeter may change.

Teacher's Note:
1. Same paper means same area.
2. Try it with a real paper chit to see the perimeter change.

Answer: (a) 7 cm

Explanation:
1. Length of the rod = perimeter of the rectangle = 2 × (9 + 5) = 28 cm.
2. The same rod makes the square, so 4 × side = 28 cm.
3. Side = 28 ÷ 4 = 7 cm.

Teacher's Note:
1. The rod's length does not change when it is re-bent.
2. 28 cm is the perimeter, not the side.

Answer: (d) A is false, but R is true.

Explanation:
1. A 6 cm × 2 cm rectangle and a 4 cm × 4 cm square both have perimeter 16 cm.
2. But their areas are 12 sq cm and 16 sq cm, which are different. So A is false.
3. R correctly says what perimeter and area measure, so R is true.

Teacher's Note:
1. One counterexample is enough to show A is false.
2. Equal boundaries can enclose different regions.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. Area = \( \frac{1}{2} \) × 8 × 5 = 20 sq cm, so A is true.
2. R is a true statement about the perimeter of a triangle.
3. But A is about area, and R is about perimeter, so R does not explain A.

Teacher's Note:
1. Both can be true and still be unrelated.
2. A triangle is half of the rectangle around it.

Answer: (c) Both statements are true

Explanation:
1. Rectangles 1 × 24 and 4 × 6 both have area 24, but perimeters 50 and 20. Statement I is true.
2. A 6 × 2 rectangle and a 4 × 4 square both have perimeter 16, but areas 12 and 16. Statement II is true.
3. So both statements are true.

Teacher's Note:
1. Area and perimeter are independent measures.
2. Give an example for each statement.

Answer: (b) Only Statement II is true

Explanation:
1. A portion smaller than half a square is ignored, not counted as one. Statement I is false.
2. A portion that is exactly half a square is counted as \( \frac{1}{2} \) square unit. Statement II is true.
3. So only Statement II is true.

Teacher's Note:
1. Less than half: ignore. More than half: count 1.
2. Exactly half: count ½.

Answer: (c) Rs 7,000

Explanation:
1. The fence goes along the boundary, so find the perimeter: 2 × (60 + 40) = 200 m.
2. Cost = 200 × 35 = Rs 7,000.

Teacher's Note:
1. Fencing is paid for by length.
2. Rs 84,000 comes from wrongly using the area.

Answer: (d) 14 sq m

Explanation:
1. Area of the floor = 6 × 5 = 30 sq m.
2. Area of the carpet = 4 × 4 = 16 sq m.
3. Uncovered area = 30 − 16 = 14 sq m.

Teacher's Note:
1. Whole minus covered part gives the uncovered part.
2. Find both areas before subtracting.

Answer: (b) 12 square units

Explanation:
1. The triangle just fits inside a rectangle 6 units long and 4 units high.
2. That rectangle covers 6 × 4 = 24 square units.
3. The triangle is half of it: 24 ÷ 2 = 12 square units.

Teacher's Note:
1. Draw the enclosing rectangle and halve its area.
2. 24 is the rectangle, not the triangle.

Answer: (c) Both cards have the same perimeter, but Card Q has the greater area.

Explanation:
1. Card P: perimeter = 2 × (6 + 2) = 16 cm, area = 6 × 2 = 12 sq cm.
2. Card Q: perimeter = 4 × 4 = 16 cm, area = 4 × 4 = 16 sq cm.
3. So both have the same perimeter, but Card Q has the greater area.

Teacher's Note:
1. Work out both measures for both cards.
2. The square encloses more area for the same boundary.

Answer: (a) (i)-(q), (ii)-(r), (iii)-(s), (iv)-(p)

Explanation:
1. Square: 4 × 6 = 24 cm (q). Rectangle: 2 × (9 + 4) = 26 cm (r).
2. Equilateral triangle: 3 × 10 = 30 cm (s). Regular pentagon: 5 × 4 = 20 cm (p).
3. So the match is (i)-(q), (ii)-(r), (iii)-(s), (iv)-(p).

Teacher's Note:
1. Work out all four perimeters first.
2. Then pick the option that fits all four.

Answer: (d) Neither statement is true

Explanation:
1. Side s becomes 2s. Perimeter changes from 4s to 8s: only twice as much. Statement I is false.
2. Area changes from s × s to 2s × 2s = 4 × (s × s): four times as much. Statement II is false.
3. So neither statement is true.

Teacher's Note:
1. Test with side 1 cm and side 2 cm.
2. The two statements have the multipliers swapped.

Answer: (c) A is true, but R is false.

Explanation:
1. Both areas are 36 square units. Perimeters: 2 × (1 + 36) = 74 units and 4 × 6 = 24 units. So A is true.
2. A itself shows two figures with the same area and different perimeters, so the perimeter does not depend only on the area. R is false.

Teacher's Note:
1. A counterexample to R is right inside A.
2. Shape matters for perimeter.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The new square adds 4 unit edges to the boundary.
2. The shared side hides one edge of the new square and one edge of the old figure: 2 edges are lost.
3. Change = 4 − 2 = 2 units, so A is true, R is true and R explains A.

Teacher's Note:
1. Count edges added and edges hidden.
2. Touching along two sides would hide 4 edges instead.

Answer: (d) 54 sq cm

Explanation:
1. Lower rectangle: 10 cm × 3 cm = 30 sq cm.
2. Upper rectangle: width 6 cm, height 7 − 3 = 4 cm, so 6 × 4 = 24 sq cm.
3. Total area = 30 + 24 = 54 sq cm.

Teacher's Note:
1. Find a missing side by subtracting.
2. Split with one horizontal line.

Answer: (b) (i)-(s), (ii)-(r), (iii)-(q), (iv)-(p)

Explanation:
1. 2 × (1 + 24) = 50 (s); 2 × (2 + 12) = 28 (r).
2. 2 × (3 + 8) = 22 (q); 2 × (4 + 6) = 20 (p).
3. So the match is (i)-(s), (ii)-(r), (iii)-(q), (iv)-(p).

Teacher's Note:
1. The thinner the rectangle, the longer its boundary.
2. The rectangle closest to a square has the least perimeter.

Answer: (a) 20 units

Explanation:
1. The perimeter is greatest when as few edges as possible are hidden, that is, when the squares form one straight strip.
2. A 1 × 9 strip has perimeter 2 × (1 + 9) = 20 units.
3. The 3 × 3 square gives the least perimeter, 12 units.

Teacher's Note:
1. Each shared side hides 2 unit edges.
2. A strip shares the fewest sides.