Sheet 3 of 10 · Maths
Area, perimeter and volume
Formulas for 2D shapes, cuboids and circles. 10 rules, each with a worked example.
Perimeter and area
Perimeter
Perimeter equals add up all the sides
- Rectangle: P = 2 × (length + width)
Example8 cm by 5 cm rectangle: P = 2 × (8 + 5) = 26 cmArea of a rectangle
Area equals length × width
- Area is measured in square units: cm², m²
Example8 cm × 5 cm = 40 cm²Area of a triangle
Area equals ½ × base × height
- Use the perpendicular (straight-up) height, not the sloping side
Exampleb = 10 cm, h = 6 cm: ½ × 10 × 6 = 30 cm²Area of a parallelogram
Area equals base × height
- Again use the perpendicular height, not the slanted side
Exampleb = 9 cm, h = 4 cm: 9 × 4 = 36 cm²Compound shapes
Split into rectangles, find each area, then add
ExampleL-shape made of a 10 cm × 4 cm and a 3 cm × 5 cm rectangle: 40 + 15 = 55 cm²Tip: Missing side? Opposite sides of the whole shape add up to the same length.
Volume and surface area
Volume of a cuboid
Volume equals length × width × height
- Volume is measured in cubic units: cm³, m³ · 1 litre = 1000 cm³
Example6 cm × 4 cm × 3 cm = 72 cm³Volume of a cube
Volume = side × side × side = s³
Examples = 5 cm: 5 × 5 × 5 = 125 cm³Surface area of a cuboid
SA equals 2 × (lw + lh + wh)
- Add the areas of all 6 faces: they come in 3 matching pairs
Example6 × 4 × 3 cuboid: 2 × (24 + 18 + 12) = 2 × 54 = 108 cm²
Circles
Parts of a circle
Diameter = 2 × radius (d = 2r)
- Radius: centre to edge · Diameter: edge to edge through the centre
- Circumference: the distance all the way round
Circumference and area
C = πd = 2πr · A = πr²
- Only some 11+ tests use π: use 3.14, or the value the question gives
Exampler = 5 cm, π = 3.14: C = 3.14 × 10 = 31.4 cm · A = 3.14 × 25 = 78.5 cm²
Want the full explanation?
The study guide goes through each rule step by step, with more examples.