What is the area formula for a trapezoid with bases b1 and b2 and height h?

What is the area formula for a trapezoid with bases b1 and b2 and height h?

• A. A = (b1 + b2) h
• B. A = b1 h + b2 h
• C. A = 1/2 (b1 + b2) h
• D. A = (b1 - b2) h

Answer: (C)

Area of a trapezoid is found by multiplying the height by the average width across the shape. The height h is the perpendicular distance between the two bases, and the width changes from b1 to b2 as you move from one base to the other. Since the width varies linearly, the average width is (b1 + b2)/2. Multiplying this average width by the height gives the area: A = h * (b1 + b2)/2, which is the same as A = 1/2 (b1 + b2) h. This reflects how the overall space scales with height and the two base lengths.

Area of a trapezoid is found by multiplying the height by the average width across the shape. The height h is the perpendicular distance between the two bases, and the width changes from b1 to b2 as you move from one base to the other. Since the width varies linearly, the average width is (b1 + b2)/2. Multiplying this average width by the height gives the area: A = h * (b1 + b2)/2, which is the same as A = 1/2 (b1 + b2) h. This reflects how the overall space scales with height and the two base lengths.