Knowledge Organiser: Area of Parallelograms & Trapeziums
Key Terms
- Parallelogram: Quadrilateral with two pairs of parallel sides
- Trapezium: Quadrilateral with exactly one pair of parallel sides
- Perpendicular height: The vertical height at 90° to the base (NOT the slant side)
- Parallel sides: The two sides labelled a and b in the trapezium formula
Must-Know Facts
- Parallelogram area = base × perpendicular height (same as rectangle)
- Trapezium: add the parallel sides first, then multiply by height, then halve
- Height is ALWAYS perpendicular (90°): never use the slanted side
- Trapezium formula works because it finds the average width times height
- Area is always in square units: cm², m²
Key Formulas
- Parallelogram: A = b × h
- Trapezium: A = ½ × (a + b) × h
- Reverse (find height): h = A ÷ b
Common Mistakes
- Parallelogram: using slant height: Must use the perpendicular height, not the slant side
- Trapezium: wrong bases: a and b are the two PARALLEL sides: identify these carefully from the diagram
- Forgetting the ½ in trapezium: A = ½(a + b)h: the ½ is always required
- Units: Area answers must be in square units (cm², m²): never linear units
Worked Examples
Find the area of a parallelogram with base 9 cm and perpendicular height 4 cm. Step 1 Write the formula Area = base × height Step 2 Substitute and calculate Area = 9 × 4 = 36 cm²
Worked Examples
Find the area of a trapezium with parallel sides 8 cm and 12 cm, and height 5 cm. Step 1 Write the formula Area = ½ × (a + b) × h Step 2 Add the parallel sides a + b = 8 + 12 = 20 Step 3 Apply the formula Area = ½ × 20 × 5 Area = ½ × 100 = 50 cm²
Worked Examples
A parallelogram has area 56 cm² and base 8 cm. Find the height. Step 1 Set up the equation Area = base × height 56 = 8 × height Step 2 Solve for height height = 56 ÷ 8 = 7 cm