Which formula is incorrect for calculating the area of a trapezoid?

Which formula is incorrect for calculating the area of a trapezoid?

• A. A = (1/2)h(b1 + b2)
• B. A = (1/2)(b1 - b2)h
• C. A = (1/2)(b1 + b2)h
• D. A = (1/3)(b1 + b2)h

Answer: (B)

The area of a trapezoid comes from averaging the two parallel sides (the bases) and multiplying by the height—the distance between the bases. So the area is the height times the average of the bases: A = h * ((b1 + b2) / 2) = (1/2)(b1 + b2)h. Using the difference of the bases would not reflect how area grows with width; if the bases are equal, you still have a rectangle with area base × height, not zero. For example, with bases 6 and 2 and height 4, the correct area is ((6+2)/2)×4 = 16, while a formula with (b1 − b2) would give (6−2)/2×4 = 8, which is not correct.

The area of a trapezoid comes from averaging the two parallel sides (the bases) and multiplying by the height—the distance between the bases. So the area is the height times the average of the bases: A = h * ((b1 + b2) / 2) = (1/2)(b1 + b2)h. Using the difference of the bases would not reflect how area grows with width; if the bases are equal, you still have a rectangle with area base × height, not zero. For example, with bases 6 and 2 and height 4, the correct area is ((6+2)/2)×4 = 16, while a formula with (b1 − b2) would give (6−2)/2×4 = 8, which is not correct.