1. **Problem Statement:** We need to find a formula for the area of trapezoid ABCD in terms of $a$, $b$, and $h$. The trapezoid has one pair of parallel sides: $AB$ and $DC$. Side $AB$ has length $a$, side $DC$ has length $b$, and $h$ is the height perpendicular from $B$ to $DC$. 2. **Formula for Area of a Trapezoid:** The area $A$ of a trapezoid is given by the formula: $$A = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}$$ This means: $$A = \frac{1}{2} (AB + DC) \times h$$ 3. **Substitute the given lengths:** Since $AB = a$ and $DC = b$, substitute these into the formula: $$A = \frac{1}{2} (a + b) \times h$$ 4. **Explanation:** - The trapezoid has two parallel sides $a$ and $b$. - The height $h$ is the perpendicular distance between these parallel sides. - The area is the average length of the parallel sides multiplied by the height. 5. **Final formula:** $$\boxed{A = \frac{1}{2} (a + b) h}$$ This formula correctly calculates the area of trapezoid ABCD in terms of $a$, $b$, and $h$.