Area of Parallelograms and Trapeziums

Area of a parallelogram

If you cut a triangle off one end of a parallelogram and move it to the other end, you make a rectangle. That is why:

Here $b$ is the base and $h$ is the perpendicular height — not the slant height.

Area of a trapezium

A trapezium has one pair of parallel sides, labelled $a$ (top) and $b$ (bottom). Its area formula is:

Think of it as: find the average of the two parallel sides, then multiply by the height. This works because two identical trapeziums fit together to make a parallelogram of base $(a + b)$.

See it: rearrange into a rectangle

Choose Parallelogram and press Transform to watch a triangle slice off one end and slide across, forming a rectangle. Use the slant slider to try different shapes — the trick always works. Switch to Trapezium to see how two copies fit together into a rectangle of width (a + b).

Watch it work

Question: Find the area of a trapezium with parallel sides $a = 6 \, \text{cm}$ and $b = 10 \, \text{cm}$, and height $h = 4 \, \text{cm}$.

Have a go