Which expression correctly computes the area of a trapezoid with bases b1 and b2 and height h?

Which expression correctly computes the area of a trapezoid with bases b1 and b2 and height h?

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

Answer: (D)

The area of a trapezoid depends on its height and the widths of its two parallel sides. Think of the width across the shape varying linearly from one base to the other; the area is effectively the height times the average width between the bases. That gives the area formula A = h times the average of the bases, which is A = h · (b1 + b2)/2, or equivalently A = (1/2)(b1 + b2)h. This makes intuitive sense: if the two bases are equal, the shape is a rectangle with area b1·h, and the formula reduces to (b1 + b1)/2 · h = b1·h. The other expressions don’t fit the geometry: using the difference (b1 − b2)h would not consistently represent area and can even be negative, while summing the products b1h + b2h effectively double-counts the space.

The area of a trapezoid depends on its height and the widths of its two parallel sides. Think of the width across the shape varying linearly from one base to the other; the area is effectively the height times the average width between the bases. That gives the area formula A = h times the average of the bases, which is A = h · (b1 + b2)/2, or equivalently A = (1/2)(b1 + b2)h.

This makes intuitive sense: if the two bases are equal, the shape is a rectangle with area b1·h, and the formula reduces to (b1 + b1)/2 · h = b1·h. The other expressions don’t fit the geometry: using the difference (b1 − b2)h would not consistently represent area and can even be negative, while summing the products b1h + b2h effectively double-counts the space.