Maths worksheets · lesson 62 of 64 · free

Mensuration: trapezium, cuboid and cube — Maths worksheet

A trapezium has one pair of parallel sides; its area is half the sum of the parallel sides × the distance between them. A rhombus has area half the product of its diagonals. The total surface area of a cuboid is the area of its 6 faces, 2(lb + bh + hl), and a cube has 6 equal squares, 6a². The four walls of a room have area 2h(l + b).

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The method

Flat parts add up — “a surface area is the total of the flat faces you can see”

  1. Trapezium: area = ½ × (a + b) × h. Rhombus: area = ½ × d₁ × d₂.
  2. Cuboid: total surface area = 2(lb + bh + hl); four walls = 2h(l + b).
  3. Cube: total surface area = 6a²; edge = √(surface area ÷ 6).
  4. Missing height of a trapezium = 2 × area ÷ (a + b).

Use it for: Painting rooms, wrapping boxes, fields shaped like a trapezium, and the mensuration chapter of Class 8 maths.

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Worked example: A trapezium has parallel sides of 12 cm and 8 cm, and the distance between them is 5 cm. What is its area (in square cm)? → 50

  1. Area = ½ × (12 + 8) × 5 = ½ × 20 × 5.
  2. 10 × 5 = 50.

Check: 2 × 50 ÷ (12 + 8) = 100 ÷ 20 = 5, the height ✓

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🏁 Lesson 62 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Class 8 Maths Worksheet: Mensuration

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