Areas of triangles, parallelograms and trapezia
Edexcel 1MA1 examines this on every paper across both tiers. Foundation focuses on direct application; Higher applies these formulae inside compound shapes and worded contexts.
Triangle
A = (1/2) × base × perpendicular height
The height MUST be perpendicular to the chosen base, not a slant edge.
For a right-angled triangle, the two perpendicular sides serve as base and height.
Higher tier — sine area rule
A = (1/2) × ab × sinC, where a and b are two sides and C is the included angle. Especially useful for non-right-angled triangles.
Parallelogram
A = base × perpendicular height
Like a triangle, the height is perpendicular to the chosen base, not the slant edge.
Trapezium
A = (1/2) × (a + b) × h
a and b are the parallel sides; h is the perpendicular distance between them.
A handy memory aid: average the two parallel sides, then multiply by the height.
Compound shapes
Decompose into rectangles, triangles, parallelograms, or trapezia. Sum the parts.
For "subtract a hole" shapes (e.g. a rectangle with a triangular notch), find the outer area and subtract the missing piece.
Units
Areas always have square units (cm², m², mm², m²). On compound shapes ensure all linear dimensions share the same unit before computing.
Common Edexcel mark-scheme phrasing
- M1 for correct formula or correct decomposition.
- M1 for substituting correct values.
- A1 for the area with correct units.
⚠Common mistakes— Common errors
- Using a slant edge as the height (only the perpendicular height counts).
- Forgetting (1/2) on a triangle.
- Mixing units (e.g. cm and mm without converting).
- Stating area without square units.
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