The area of a trapezoid with height h and bases b1 and b2 is:

Prepare for the Geometry CBE Exam with targeted resources. Access interactive quizzes and detailed explanations to master geometric concepts effectively and excel in your test!

The area of a trapezoid scales with the height and the average width between the two bases. As you move from one base to the other, the width changes linearly from b1 to b2, so the average width across the height is (b1 + b2) / 2. Multiply this by the height h to get the area: A = h * (b1 + b2) / 2, which is the same as (1/2) h (b1 + b2).

This matches the idea that slicing the trapezoid into many thin horizontal strips yields lengths that blend from b1 to b2; the mean of those lengths is (b1 + b2)/2, and multiplying by the height gives the total area.

Why the other expressions don’t fit: using h times just one base assumes the width stays constant at that base, which isn’t true for a trapezoid. The product b1*b2/2 corresponds to a different shape (like a right triangle with legs b1 and b2), not this trapezoid. The difference b1 - b2 is a length, not an area.