Area of standard 2D shapes
OCR J560 expects fluent recall of every standard area formula. These appear on every paper across both tiers.
The core formulae
| Shape | Area formula | Notes |
|---|---|---|
| Rectangle | length × width | Square is a special case (side²). |
| Triangle | ½ × base × perpendicular height | Height must be perpendicular to base. |
| Parallelogram | base × perpendicular height | NOT base × slanted side. |
| Trapezium | ½ × (a + b) × h | a, b are parallel sides; h is perpendicular distance. |
| Kite | ½ × diagonal₁ × diagonal₂ | Same formula as a rhombus. |
| Circle | π × r² | Use π button or 3.14 if specified. |
Triangle — alternative formulae (Higher)
When you don't have the perpendicular height:
- Trigonometry: Area = ½ × a × b × sinC, where C is the angle between sides a and b.
- Heron's formula: not on the GCSE syllabus, but useful as a check.
Compound shapes
Most OCR Foundation questions involve compound shapes — split into rectangles, triangles, and trapezia, find each area, and sum or subtract as needed.
✦Worked example— Worked example — trapezium
A trapezium has parallel sides 8 cm and 14 cm, perpendicular distance between them 6 cm.
Area = ½ × (8 + 14) × 6 = ½ × 22 × 6 = 66 cm².
✦Worked example— Worked example — compound
An "L"-shape is a 10 × 8 rectangle with a 4 × 3 rectangle removed from one corner.
Area = (10 × 8) − (4 × 3) = 80 − 12 = 68 cm².
OCR mark scheme conventions
- M1 for the correct formula or correct decomposition.
- A1 for the substitution.
- A1 for the final answer with units (cm², m², etc.).
- "Show your working" — formula must be visible to earn M1.
⚠Common mistakes
- Using the slanted side of a parallelogram instead of the perpendicular height.
- Forgetting the ½ in the triangle or trapezium formula.
- Reporting area without squared units (cm² not cm).
- Getting confused on a trapezium with the parallel sides — they are the parallel edges, not just any two opposite sides.
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves