Which formula expresses the area of a trapezoid?

• A. A = base * height
• B. A = π r^2
• C. A = 1/2*(b1 + b2) * h
• D. A = (b1 - b2) * h

Answer: (C)

Area of a trapezoid is found by height times the average of the two bases. The two bases, b1 and b2, are parallel and the distance between them is h. Because the width of a horizontal slice through the shape changes smoothly from b1 at one end to b2 at the other, the effective width across the height is the average: (b1 + b2)/2. Multiply that by the height to get the total area: A = 1/2 * (b1 + b2) * h. The other formulas correspond to different shapes—base times height would give a rectangle, πr^2 is a circle, and (b1 − b2) × h doesn’t describe area for a trapezoid.