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Area and volume formulas flash cards

Flash cards for geometry formulas: area and perimeter of 2D shapes, circles, sectors and arcs, and the volume and surface area of prisms, cylinders, cones, pyramids and spheres.

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The cards, front and back

  1. 1
    Front

    Area of a rectangle

    Back

    Area = length × width. Perimeter = 2 × (length + width).

  2. 2
    Front

    Area of a triangle

    Back

    Area = ½ × base × perpendicular height. The height must be at right angles to the base.

  3. 3
    Front

    Area of a parallelogram

    Back

    Area = base × perpendicular height (not the slanted side).

  4. 4
    Front

    Area of a trapezium (trapezoid)

    Back

    Area = ½ × (a + b) × h, where a and b are the parallel sides and h is the perpendicular distance between them.

  5. 5
    Front

    Circumference of a circle

    Back

    C = 2πr or C = πd, where r is the radius and d is the diameter.

  6. 6
    Front

    Area of a circle

    Back

    A = πr². Square the radius first, then multiply by π.

  7. 7
    Front

    Area of a sector

    Back

    Area = (θ ÷ 360) × πr², where θ is the angle at the centre in degrees.

  8. 8
    Front

    Length of an arc

    Back

    Arc length = (θ ÷ 360) × 2πr, where θ is the angle at the centre in degrees.

  9. 9
    Front

    Pythagoras' theorem

    Back

    In a right-angled triangle, a² + b² = c², where c is the hypotenuse, the longest side, opposite the right angle.

  10. 10
    Front

    Volume of a cuboid

    Back

    Volume = length × width × height.

  11. 11
    Front

    Volume of a prism

    Back

    Volume = area of cross-section × length. This works for any prism, including triangular prisms and cylinders.

  12. 12
    Front

    Volume of a cylinder

    Back

    V = πr²h, the area of the circular end times the height.

  13. 13
    Front

    Curved and total surface area of a cylinder

    Back

    Curved surface area = 2πrh. Total surface area = 2πr² + 2πrh, adding the two circular ends.

  14. 14
    Front

    Volume of a cone

    Back

    V = ⅓πr²h, one third of the volume of a cylinder with the same base and height.

  15. 15
    Front

    Curved surface area of a cone

    Back

    Curved surface area = πrl, where l is the slant height. Add πr² for the base to get the total surface area.

  16. 16
    Front

    Volume of a pyramid

    Back

    V = ⅓ × area of base × perpendicular height.

  17. 17
    Front

    Volume of a sphere

    Back

    V = (4 ÷ 3)πr³.

  18. 18
    Front

    Surface area of a sphere

    Back

    Surface area = 4πr².

  19. 19
    Front

    What units do area and volume use?

    Back

    Area uses square units, such as cm² or m². Volume uses cubic units, such as cm³ or m³. Capacity is often given in millilitres or litres, where 1 cm³ = 1 ml.

  20. 20
    Front

    A cylinder has radius 3 cm and height 10 cm. What is its volume?

    Back

    V = πr²h = π × 9 × 10 = 90π, which is about 282.7 cm³.

  21. 21
    Front

    How do you find the area of a compound shape?

    Back

    Split it into simple shapes such as rectangles and triangles, find each area, then add them (or subtract any parts that are cut out).

  22. 22
    Front

    What happens to area and volume when a shape is enlarged by scale factor k?

    Back

    Lengths are multiplied by k, areas by k² and volumes by k³.

How to use this template

This deck puts the area, perimeter, surface area and volume formulas from school geometry in one place. It covers rectangles, triangles, parallelograms and trapeziums, circles, sectors and arcs, Pythagoras' theorem, cuboids, prisms, cylinders, cones, pyramids and spheres, units, a worked cylinder example, compound shapes and the effect of enlargement. It suits Year 7 to Year 11 maths, GCSE and IGCSE maths at foundation and higher tier, middle school and high school geometry, and adults returning to maths for a test or a trade course. Learn the formulas in Learn mode, then switch to Test mode and let spaced repetition bring back any formula you forget. Print it double-sided as a handy formula pack.

Tips

  • Sketch the shape on the back of each card in your notes, and label the lengths used in the formula.
  • Group the formulas: prisms (cross-section × length) and pointed shapes (one third of the matching prism).
  • Check which formulas your exam gives you on a formula sheet and which ones you must learn by heart.
  • Keep π in your answer until the last step, or use the π button, to avoid rounding errors.
  • Always check whether a question gives the radius or the diameter before you start.

Make it fit

  • Use the word your course uses, trapezium or trapezoid, and delete the other.
  • Add a worked example for each formula with your own numbers.
  • Make reverse cards with the formula on the front and the shape on the back.
  • Add frustums or radians for sectors if you are on an advanced course.

Updated October 28, 2026

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