PSAT Math Multiple-Choice Question 672: Answer and Explanation

Question: 672

The formula for the area of a trapezoid is , where B₁ and B₂ are the bases of the trapezoid and H is its height. If the mean of the bases of the trapezoid is twice the height and if the area of the trapezoid is 72 square inches, what is the trapezoid's height in inches?

• A. 6
• B.
• C. 24
• D. 36

Correct Answer: A

Explanation:

(A) This problem mentions the "mean of the bases." Notice that , the first part of the area formula, is another way of saying the mean of the bases. Since the mean of the bases is twice the height, we can replace this part of the formula with 2H:

The area is 72, so plug this in for A and solve for H:

72 = 2H²

Divide by 2:

36 = H²

Take the square root of both sides to arrive at the answer 6 = H, which is choice (A).