Area of a parallelogram
Base times perpendicular height; the slanted sides do not matter.
Calculator
The live calculator needs JavaScript. The worked example below shows the same steps it would.
See it move
- Area = b × h = 36
- The shaded triangle slides across to the other end, making a 9 × 4 rectangle.
What the symbols mean
- the area
- the base: one of the sides
- the perpendicular height between the base and the opposite side
When to use it
Use it for any four-sided shape with two pairs of parallel sides: parallelograms, rhombuses, and rectangles (where the height is just the other side). It is also why shearing a shape sideways does not change its area.
Worked example
A parallelogram has a base of 9 cm and a perpendicular height of 4 cm. What is its area? (b = 9, h = 4)
Start from the formula.
Substitute = , = and work it out.
Answer A = 36 cm²
Why it works
Cut the triangle off one end and slide it to the other (the shaded piece in the graph). The parallelogram becomes a rectangle with the same base and the same height.
Common mistakes
- Multiplying the base by the slanted side. That overestimates the area unless the shape is a rectangle.
- Halving the answer as if it were a triangle.