Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the formula for the area of a trapezoid?

1. A=bh

2. A=(1/2)h(b₁+b₂)

3. A=πr²

4. A=l*w

The correct answer is: A=(1/2)h(b₁+b₂)

The formula for the area of a trapezoid is derived from its geometric properties. A trapezoid has two parallel sides, often referred to as the bases. When finding the area, the formula takes into consideration both of these bases and the height of the trapezoid, which is the perpendicular distance between the bases. The correct formula, which is represented as \( A = \frac{1}{2} h (b_1 + b_2) \), is a direct application of averaging the lengths of the two bases. Here, \( b_1 \) and \( b_2 \) represent the lengths of the two bases, and \( h \) is the height. The \( \frac{1}{2} \) factor is included because the area of a trapezoid can be thought of as the average length of the bases multiplied by the height, which corresponds to the area of a rectangle that would enclose the trapezoid if extended. This understanding distinguishes it from the formulas for other shapes provided in the options, such as the area of a rectangle or a circle, which utilize different parameters and structures for their calculations. Thus, the formula for the area of a trapezoid effectively captures its unique geometry