Geometry and Measurement
Geometry and Measurement
This domain tests shape properties, angle relationships, perimeter, area, volume, similarity, coordinate geometry, and unit conversion. Many questions combine a diagram-free description with a measurement conversion, so track units as you calculate.
Core rules
- Angles on a straight line sum to 180°; angles around a point sum to 360°; vertically opposite angles are equal.
- Triangle angles sum to 180°. In an isosceles triangle, base angles are equal.
- Pythagoras: a² + b² = c² for a right triangle with hypotenuse c.
- Area: rectangle bh; triangle ½bh; circle πr². Circumference is 2πr.
- Volume: prism area of cross-section × length; cylinder πr²h.
- Similar figures: corresponding lengths scale by k, areas by k², volumes by k³.
- Coordinate geometry: gradient (y₂ - y₁)/(x₂ - x₁); distance √((x₂ - x₁)² + (y₂ - y₁)²).
Worked example
A rectangle is 6 cm by 8 cm. A similar rectangle has perimeter 42 cm. What is its area? Original perimeter = 2(6 + 8) = 28 cm. Scale factor k = 42/28 = 1.5. Area scale factor = k² = 2.25. Original area = 48 cm², so new area = 48 × 2.25 = 108 cm².
Traps
- Using diameter instead of radius in circle formulas.
- Mixing units before calculating, such as centimetres with metres.
- Assuming area scales by k rather than k².
- Applying Pythagoras to a non-right triangle.
- Confusing perimeter and area labels.