Area and volume formulae · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Area of trapezia and volume of prisms

Mathematics · Geometry · ages 11-14
Name ______________________   Date ____________

  1. What is the formula for the area of a trapezium with parallel sides a and b and height h?

    • A = ½(a + b) × h
    • A = a × b × h
    • A = ½ × a × b

  2. A cylinder's volume formula, π × r² × h, comes from treating it like a prism with a circular cross-section.

    Circle one:   True   False

  3. What do you multiply a prism's cross-sectional area by to find its volume?

    • The length of the prism
    • The area of one end again
    • The number of faces the prism has

  4. A cuboid shaped box is 5 cm long, 3 cm wide and 2 cm tall. What is its volume in cubic centimetres?

    Answer: ______________

  5. A cylinder has radius 3 cm and height 10 cm. Which calculation gives its volume using π × r² × h?

    • π × 3² × 10
    • π × 3 × 10²
    • π × (3 × 10)²

  6. A garden bed is shaped like a trapezium. The two parallel sides are 8 m and 5 m long, and the distance between them is 4 m. What is the area of the garden bed in square metres?

    Answer: ______________

  7. Prism A measures 2 cm by 3 cm by 2 cm. Prism B measures 3 cm by 2 cm by 4 cm. Which statement is true?

    • Prism A has double the volume of Prism B
    • Prism B has double the volume of Prism A
    • Both prisms have the same volume
    • Prism B has four times the volume of Prism A

  8. A trapezium has parallel sides of 8 m and 12 m and a height of 5 m. What is its area?

    • 50 m²
    • 100 m²
    • 60 m²

  9. Two snack containers are on the table. Container 1 is a cylinder with radius 4 cm and height 6 cm. Container 2 is a cuboid 5 cm by 5 cm by 10 cm. Using 3.14 for pi, which container holds more?

    • Container 1, the cylinder
    • Container 2, the cuboid
    • They hold exactly the same amount
    • You cannot tell without weighing them

  10. Zara found the area of a trapezium with parallel sides 6 cm and 10 cm and height 5 cm by working out (6 + 10 + 5) ÷ 2. What went wrong?

    • She added the height into the average instead of multiplying it in separately
    • She mixed up which two lengths are the parallel sides
    • She used the perimeter instead of the area formula
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Area of trapezia and volume of prisms W1-mt_tAJH5BrpOx-s1

  1. A = ½(a + b) × h · You average the two parallel sides, then multiply by the height between them.
  2. True · The circle's area, π × r², plays the same role as any prism's cross-sectional area.
  3. The length of the prism · The cross-section stays the same all the way through, so volume is cross-sectional area times length.
  4. 30 · A cuboid is a prism with a rectangle as its cross-section, so its volume is the cross-sectional area times the length.
  5. π × 3² × 10 · Only the radius is squared. The height is multiplied in separately, not squared or combined with the radius first.
  6. 26 · Two copies of the trapezium fit together to make a parallelogram with base (8 + 5) and height 4, so one trapezium is half of that parallelogram.
  7. Prism B has double the volume of Prism A · Working out each volume with length x width x height shows Prism B is exactly double Prism A.
  8. 50 m² · ½ × (8 + 12) × 5 = 50 m². Forgetting the ½ gives 100, and using only one side instead of the average gives 60.
  9. Container 1, the cylinder · Both shapes are prisms, so compare their volumes by multiplying each cross-sectional area by its height or length.
  10. She added the height into the average instead of multiplying it in separately · The height should be multiplied in after averaging the parallel sides: ½ × (6 + 10) × 5 = 40 cm², not folded into the average.
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