Sheet № 166 · Foundation + Higher · AQA · Edexcel · OCR
Area of a Parallelogram –
The parallelogram is a shape that trips up many GCSE students because it looks like a slanted rectangle — and the temptation is to multiply the two visible side lengths. The correct formula uses the perpendicular height, not the slant side.
§Key definitions
Question:
A parallelogram has a base of 8 cm and a perpendicular height of 5 cm. Find its area.
Q1 (Foundation):
A parallelogram has a base of 12 cm and a perpendicular height of 7 cm. Find its area.
Q2 (Foundation):
A parallelogram has a base of 9.5 cm and a perpendicular height of 4 cm. Find its area.
Q3 (Higher):
A parallelogram has an area of 108 cm². The perpendicular height is 9 cm. The slant side is 11 cm. Find the base.
§Formulas to memorise
A = base × perpendicular height
The perpendicular height is the vertical distance between the two parallel sides, measured at right angles to the base
Multiply: A = base × perpendicular height.
A = base × height
A = 8 × 5
A = 40
h = 91 ÷ 13
h = 7
Rectangle area = 10 × 4 = 40 cm²
Parallelogram area = 10 × 3 = 30 cm²
Worked example
A parallelogram has a base of 8 cm and a perpendicular height of 5 cm. Find its area. [DIAGRAM: shape | variant=parallelogram | base=8 cm | height=5 cm]
Working: A = base × height A = 8 × 5 A = 40
⚠ Common mistakes
- ✗Using the slant height instead of the perpendicular height. The slant edge is a side of the shape, not the height. The perpendicular height is always shorter than the slant side and is marked with a right-angle symbol.
- ✗Confusing with a trapezium. A parallelogram has two pairs of parallel sides, not one. You do not need to average the sides — both parallel sides are equal, so just use one as the base.
- ✗Halving the answer. Unlike a triangle, there is no ½ in the parallelogram formula. If you halve, you have calculated the area of a triangle instead.
- ✗Forgetting square units. Always state your answer in cm², m², or the appropriate square unit.
- ✗Multiplying two adjacent sides. Two adjacent sides of a parallelogram are not the same as base and height unless the shape is a rectangle.
✦ Exam tips
- →The parallelogram formula is not always on the formula sheet — learn it by heart.
- →If a right-angle symbol appears inside the shape, that line is the perpendicular height.
- →When the perpendicular height is outside the shape (drawn as an extension), it is still valid — this happens with very slanted parallelograms.
- →If you are given the side lengths and an angle instead of the height, you can use h = side × sin(angle) to find the perpendicular height before applying the formula.
- →Sketch the equivalent rectangle alongside the parallelogram if you find it helpful to visualise the area.