What is the area formula for a trapezoid?

• A. a = 1/2(b1 + b2)h
• B. p = sum of all 3 sides
• C. All sides are congruent
• D. Diagonals are perpendicular

Answer: (A)

The area of a trapezoid comes from using the height and the two bases. The bases are the parallel sides, call them b1 and b2, and the height is the perpendicular distance between those bases. The area is found by multiplying the height by the average of the two bases: A = h × (b1 + b2)/2, which is the same as A = (1/2)(b1 + b2)h. This works because you can imagine filling the trapezoid with a rectangle of height h and width equal to the average of the bases, or by decomposing the shape into simpler pieces whose areas sum to that same value. For example, if the bases are 6 and 4 with a height of 3, the area is 3 × (6 + 4)/2 = 3 × 5 = 15. The other statements describe perimeter, equal sides, or diagonal properties, which aren’t about finding area.