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G6 Mensuration
Math quiz helps us to enhance brains neural network.
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1) The length of a rectangle is (3x + 2) cm and its breadth is (x − 1) cm. What is the perimeter of the rectangle in terms of x?
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2) In rectangle ABCD,
If the length is increased by 2x and the breadth is decreased by x, then find the new perimeter.
1000 cm³ = 1 L → 2500 ÷ 1000 = 2.5 L
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3) A circular field has area 154 m². What is its radius? (Use π = 3.14)
A = πr² → r² = 154 ÷ 3.14 = 49 → r = √49 = 7 m
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4) A rectangular farm is 320 m long and 185 m wide. The cost of fencing per metre is ₹36. Find:(i) the area of the farm,(ii) the cost of fencing the farm when fencing is done four times around the boundary.
A = ½ × b × h = ½ × 15 × 8 = 60 m²
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5) In the given rectangle PQRS,
If the length is decreased by x and the breadth is increased by 3x, then find the new perimeter of the rectangle.
Square = 100 cm², Circle = πr² = 3.14 × 4 = 12.56 → Remaining = 87.44 cm²
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6) A rectangular field is 60 m long and 40 m wide. A 2 m wide path is made inside along all sides. Find the area of the path.
Outer area = 60×40 = 2400, Inner = 56×36 = 2016 → Path = 384 m²
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7) A square of side 6 cm and a rectangle of 9 cm × 4 cm are given.
Which has greater area?
Square = 36 cm², Rectangle = 36 cm² → Both equal
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8) A cuboid of 10 × 5 × 2 cm is hollowed to create a box with thickness 1 cm. What is the volume of the hollow part?
Outer = 100 cm³, Inner = 8×3×0 = 24 cm³ → Hollow = 76 cm³
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9) A cube and a cuboid both have surface area of 150 cm². The cube has a side of 5 cm.
Which one has greater volume?
: Cube: V = 125 cm³, Cuboid: SA = 150 cm² but shape unknown. Volume of cube is known → Cube
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10) In rectangle WXYZ,
If the length is increased by x and the breadth is increased by 2x, find the new perimeter.
: Draw and count only outer sides → 5 + 3 + 3 + 3 + 5 + 3 = 22 cm
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11) Find the length of side of a regular pentagon when its perimeter is 95m?
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12) A cylindrical tank has radius 1.5 m and height 2 m. Find its volume. (Use π = 3.14)
πr²h = 3.14 × (1.5)² × 2 = 3.14 × 2.25 × 2 = 14.13 m³
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13) Which of the following statements is INCORRECT?
A. The area of a triangle with base 24 cm and height 10 cm is 120 cm².B. A square with perimeter 64 cm has area 256 cm².C. Since 1 cm=10 mm, 1 cm²=100 mm². Therefore, 2,500 mm² = 25 cm².D. Ramesh walks thrice around a 50 m by 30 m rectangle, while Suresh walks twice around a square of side 40 m; Ramesh covers 100 m more.
Rect = 24 cm², Semi = ½πr² = ½×3.14×4 = 6.28 cm² → Total = 30.28 cm²
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14) A square room has side 6 m. Each square tile is 1 m². How many tiles are needed to tile the whole floor?
Area = 6 × 6 = 36 m² → 36 tiles
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15) What is the area of a below square?
Area = side² = 9² = 81 cm²
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16) A rectangle and a square are placed side by side. Find total area.
Rectangle = 18 cm², Square = 9 cm² → Total = 27 cm²
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17) A square has a perimeter of 36 cm.
What is the length of one side?
Side = Perimeter ÷ 4 = 36 ÷ 4 = 9 cm
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18) A rectangular school playground measures 125 m by 95 m. The cost of fencing per metre is ₹48.
Find:(i) the area of the playground,(ii) the cost of fencing the playground when fencing is done three times around it.
SA = 6 × side² = 6 × 25 = 150 cm²
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19) A farmer has a square plot of side 20 m. He builds a 1.5 m wide path inside the peripheri.
What is the area left for farming?
Outer = 400, Inner = (20−3)² = 289 → Area for farming = 289 m²
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20) What is the area of this shape?
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