Which expression correctly represents the area of a trapezoid in terms of its two bases and height?

Which expression correctly represents the area of a trapezoid in terms of its two bases and height?

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

Answer: (A)

The area of a trapezoid is found by multiplying the height by the average of the two bases. The height is the perpendicular distance between the bases, and the bases have lengths b1 and b2. Because the trapezoid tapers from one base to the other, its area can be viewed as the height times the average width, which is (b1 + b2)/2. So the area is A = h × [(b1 + b2)/2] = 1/2 × (b1 + b2) × h. Using (b1 + b2) × h would give a value that’s too large, since it doesn’t average the two bases. Using (b1 − b2) × h would yield zero when the bases are equal, which is incorrect for a rectangle (equal bases still form a trapezoid with area bh). Using b1 × h ignores the second base entirely, also incorrect.

The area of a trapezoid is found by multiplying the height by the average of the two bases. The height is the perpendicular distance between the bases, and the bases have lengths b1 and b2. Because the trapezoid tapers from one base to the other, its area can be viewed as the height times the average width, which is (b1 + b2)/2. So the area is A = h × [(b1 + b2)/2] = 1/2 × (b1 + b2) × h.

Using (b1 + b2) × h would give a value that’s too large, since it doesn’t average the two bases. Using (b1 − b2) × h would yield zero when the bases are equal, which is incorrect for a rectangle (equal bases still form a trapezoid with area bh). Using b1 × h ignores the second base entirely, also incorrect.