Measurement, Space and Shape
What you need to understand
This domain concerns the properties of two- and three-dimensional shapes and how they behave in space. You should recognise common shapes, name their features (sides, vertices, faces, edges), understand symmetry, and be able to reason about angles - right angles, straight lines, angles at a point, and angles in triangles and quadrilaterals. You should also be able to read and interpret simple maps, plans and scale drawings, use compass directions, and understand nets of common solids. Scale drawings link measurement to shape: a scale of 1:100 means 1 cm on the plan represents 100 cm in reality.
Traps to watch for
- Angle sums. Angles on a straight line add to 180°, angles at a point add to 360°, and angles in a triangle add to 180°.
- Scale factor confusion. Multiply by the scale to go from plan to reality; divide to go the other way.
- Similar shapes. Corresponding lengths scale by the factor, but areas scale by the square of the factor.
- Nets. Check that faces meet along matching edges and that the net folds without overlap.
Worked example
A plan uses a scale of 1:200. A room measures 4.5 cm by 3 cm on the plan. What is its real area in square metres?
Real length = 4.5 × 200 = 900 cm = 9 m. Real width = 3 × 200 = 600 cm = 6 m. Area = 9 × 6 = 54 m². The trap is to scale the area by 200; the linear scale must be applied to each dimension before multiplying.
Rule of thumb
Apply the scale to lengths first, convert units, then calculate area or volume.