The area of a trapezoid with bases b1 and b2 and height h is which expression?

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

Answer: (A)

The area of a trapezoid is found by multiplying the height by the average of the two parallel sides (the bases). Since the bases are b1 and b2 and the height is h, the average of the bases is (b1 + b2)/2. Multiplying by h gives the area: 1/2 (b1 + b2) h. This also checks out in a special case: if both bases are equal, the shape is a rectangle with area bh, and the formula yields 1/2 (b + b) h = bh. The other expressions don’t match this geometric idea: using the product of the bases, or the difference of the bases, or omitting the 1/2 would not give the correct area.