Track / Stage 4 / 309 of 340 #569 of 1964

Problem 569

AMC 12 late, AIME early

Geometry Difficulty 5.0 Find the answer

$18 \cdot 120$ is the short base, height, and long base of a trapezoid, which form an arithmetic sequence. Let $k$ be the area of this trapezoid, then

Pick one

Official solution

[Solution] Let the shorter base, height, and longer base of the trapezoid be $a-d, a, a+d$ respectively. Then $k=S_{\text {trapezoid }}=\frac{1}{2}[(a-d)+(a+d)] a=a^{2}$ . By the arbitrariness of $a$ , we know that $(A),(B),(C),(D)$ are all incorrect. Therefore, the answer is $(E)$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.