Cut a parallelogram corner to corner and two equal triangles fall out — which is the whole story of $A = \tfrac{1}{2} b h$: a triangle is HALF a parallelogram, and the $\tfrac{1}{2}$ remembers the cut. Forgetting it is this lesson's headline mistake, and it always lands exactly double.

A trapezoid has two parallel sides of different lengths, $a$ and $b$. Fair is fair: use their AVERAGE. $A = \dfrac{a+b}{2} \cdot h$ — A equals a plus b, over two, times h: add the parallel sides, halve them, times the height between them. And reversing either formula is ordinary algebra with one nice rule: what was halved on the way in comes back DOUBLED on the way out — $h = \dfrac{2A}{b}$, the 2 riding on top.