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About Mensuration (Area & Volume) — Class 8 CBSE

Calculate area of trapezium, polygon, and surface area and volume of solids. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 14). On this page you can practice 61 questions across three difficulty levels — 20 easy, 20 medium, and 21 hard — each with a visual step-by-step solution, plus a timed 36-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Mensuration (Area & Volume)

  • Introduction to Mensuration: Measuring Shapes
  • Area of Trapezium and Polygons
  • Surface Area of Cube, Cuboid, and Cylinder
  • Volume of Cube, Cuboid, and Cylinder
  • Advanced Applications and Problem Solving

Interactive lesson · about 15 minutes · checkpoint question after every unit

Mensuration (Area & Volume) — solved examples for Class 8 CBSE

Example 1easy

Ravi is trying to explain the formula for the area of a trapezium. He says, "The formula A = 1/2 × h × (a + b) works because a trapezium can be thought of as a rectangle with base (a+b)/2 and height h." Which of the following statements about Ravi's reasoning is true?
  1. A)Ravi's explanation is incorrect because a trapezium cannot be simplified to a rectangle.
  2. B)Ravi's explanation is correct and accurately describes the geometric intuition behind the formula.
  3. C)Ravi's explanation is partially correct, but it should be A = h × (a + b) not 1/2 × h × (a + b).
  4. D)Ravi's explanation is incorrect; the formula involves dividing the trapezium into two triangles.

Step-by-step solution

  1. The area of a trapezium is given by A = 1/2 × h × (sum of parallel sides).
    A=1/2×h×(a+b)A = 1/2 × h × (a + b)
  2. The term (a+b)/2 represents the average length of the parallel sides. If we imagine stretching the shorter parallel side to match the longer, or vice versa, the 'effective' base length becomes the average. Multiplying this average base by the height 'h' indeed gives the area, just like a rectangle with that average base and height 'h'.
  3. Thus, Ravi's explanation correctly captures the essence of how the formula works conceptually.

Answer: Ravi's explanation is correct and accurately describes the geometric intuition behind the formula.

Example 2medium

A trapezium has parallel sides of length 12 cm and 18 cm, and the perpendicular distance between them is 7 cm. What is its area?
  1. A)105 cm²
  2. B)126 cm²
  3. C)210 cm²
  4. D)84 cm²

Step-by-step solution

  1. Identify the lengths of the parallel sides (a = 12 cm, b = 18 cm) and the height (h = 7 cm).
  2. Use the formula for the area of a trapezium:
    Area=1/2×(a+b)×hArea = 1/2 × (a + b) × h
  3. Substitute the values: Area = 1/2 × (12 + 18) × 7.
  4. Calculate: Area = 1/2 × 30 × 7 = 15 × 7 = 105 cm².

Answer: 105 cm²

Example 3hard

The parallel sides of a trapezium are in the ratio 3:5. Its height is 8 cm. If the area of the trapezium is 192 cm², what are the lengths of its parallel sides?
  1. A)15 cm, 25 cm
  2. B)21 cm, 35 cm
  3. C)12 cm, 20 cm
  4. D)18 cm, 30 cm

Step-by-step solution

  1. Let the parallel sides be 'a' and 'b'. Given a:b = 3:5, so let a = 3x and b = 5x. The height (h) is 8 cm.
  2. The area of a trapezium is given by A = (1/2) × (a + b) × h. Substitute the given values: 192 = (1/2) × (3x + 5x) × 8.
  3. Simplify and solve for x: 192 = (1/2) × (8x) × 8 => 192 = 4x × 8 => 192 = 32x => x = 192 / 32 = 6.
  4. The lengths of the parallel sides are 3x = 3 × 6 = 18 cm and 5x = 5 × 6 = 30 cm.

Answer: 18 cm, 30 cm

Practice questions on Mensuration (Area & Volume)

  1. Q1.easy

    A regular hexagon has a side length of 6 cm. If it is divided into two identical trapeziums and one rectangle, what information is essential to calculate its area using this method?
    1. A)Only the side length of the hexagon is required.
    2. B)The side length of the hexagon and the apothem (distance from center to midpoint of a side).
    3. C)The side length of the hexagon, and the height of the trapeziums formed.
    4. D)The side length of the hexagon and the perimeter of the hexagon.
    Show answer

    Answer: The side length of the hexagon, and the height of the trapeziums formed.

    Hint: When you divide a regular hexagon into these shapes, the 'height' of the trapeziums would be related to the distance between opposite sides, or the apothem if the division is different.

  2. Q2.easy

    Which of the following statements is TRUE regarding the surface area of a solid cube?
    1. A)If a cube is cut into two identical cuboids, the total surface area of the two cuboids remains the same as the original cube.
    2. B)The total surface area of a cube is the sum of the areas of its six faces.
    3. C)The surface area of a cube is always equal to its volume.
    4. D)If the side length of a cube is doubled, its surface area also doubles.
    Show answer

    Answer: The total surface area of a cube is the sum of the areas of its six faces.

    Hint: Think about the definition of surface area and how cutting a solid affects it.

  3. Q3.easy

    A farmer has a field in the shape of a quadrilateral ABCD. The diagonal AC is 24 m. The perpendiculars from B and D to AC are 8 m and 13 m respectively. What is the area of the field?
    1. A)144 m²
    2. B)216 m²
    3. C)252 m²
    4. D)336 m²
    Show answer

    Answer: 252 m²

    Hint: A general quadrilateral can be divided into two triangles by a diagonal.

  4. Q4.medium

    A rectangular water tank is 5 m long, 3 m wide, and 2 m deep. If it is filled with water up to 3/4 of its depth, what volume of water does it contain?
    1. A)30 m³
    2. B)15 m³
    3. C)22.5 m³
    4. D)10 m³
    Show answer

    Answer: 22.5 m³

    Hint: First calculate the full volume of the tank, then find 3/4 of that volume.

  5. Q5.medium

    If the lateral surface area of a cube is 100 cm², what is the total surface area of the cube?
    1. A)125 cm²
    2. B)200 cm²
    3. C)150 cm²
    4. D)250 cm²
    Show answer

    Answer: 150 cm²

    Hint: Recall the formulas for lateral surface area (LSA) and total surface area (TSA) of a cube in terms of its side.

  6. Q6.medium

    A quadrilateral field ABCD has a diagonal AC measuring 20 m. The perpendiculars dropped from vertices B and D to AC are 8 m and 10 m respectively. What is the area of the field?
    1. A)160 m²
    2. B)200 m²
    3. C)240 m²
    4. D)180 m²
    Show answer

    Answer: 180 m²

    Hint: A general quadrilateral can be divided into two triangles by a diagonal. The area of each triangle can be found using the base (diagonal) and its corresponding height (perpendicular).

  7. Q7.hard

    A field is in the shape of a polygon ABCDE. A surveyor takes measurements along a diagonal AE. Length of diagonal AE = 200 m. Perpendicular distance from B to AE is 40 m (at point F on AE), with AF = 50 m. Perpendicular distance from C to AE is 60 m (at point G on AE), with AG = 120 m. Perpendicular distance from D to AE is 30 m (at point H on AE), with AH = 160 m. Calculate the total area of the field.
    1. A)7200 m²
    2. B)7000 m²
    3. C)6900 m²
    4. D)6600 m²
    Show answer

    Answer: 6900 m²

    Hint: Divide the polygon into triangles and trapeziums by drawing perpendiculars to the diagonal AE. Calculate the area of each part and sum them up.

  8. Q8.hard

    64 identical small cubes are joined together to form a larger solid cube. If the total surface area of this larger cube is 384 cm², what is the side length of one of the small cubes?
    1. A)2 cm
    2. B)1 cm
    3. C)4 cm
    4. D)8 cm
    Show answer

    Answer: 2 cm

    Hint: First, use the surface area of the large cube to find its side length. Then, determine how many small cubes form one side of the large cube to find the small cube's side.

  9. Q9.hard

    An open rectangular water tank has outer dimensions 1.2 m long, 1 m wide, and 0.8 m high. It is made of metal sheets 2 cm thick. If the cost of painting the inner surface of the tank is ₹30.75 per square meter, what is the total cost of painting the tank? (Assume the top is open).
    1. A)₹140.25
    2. B)₹135.90
    3. C)₹128.70
    4. D)₹145.35
    Show answer

    Answer: ₹135.90

    Hint: First, calculate the inner dimensions of the tank by subtracting double the thickness from length and width, and single thickness from height (since it's open at the top). Then find the inner surface area.

These are 9 of the 61 questions available for Mensuration (Area & Volume). Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.