Question

一个长方形区域由直线 $y=a, y=-b, x=-c$ 和 $x=d$ 围成，其中 $a,b,c$ 和 $d$ 都是正数。下列哪一项表示该区域的面积？

A rectangular region is bounded by the graphs of the equations $y=a, y=-b, x=-c,$ and $x=d,$ where $a,b,c,$ and $d$ are all positive numbers. Which of the following represents the area of this region?

$ac+ad+bc+bd$

$ac-ad+bc-bd$

$ac+ad-bc-bd$

$-ac-ad+bc+bd$

$ac-ad-bc+bd$

答案：A

知识点：坐标几何矩形分配律

难度评级：900

解答：

该区域是长方形，两条边长分别为和因此面积为 $a - (-b) = a + b$ $d - (-c) = c + d.$ $(a + b)(c + d) =$ $ac + ad + bc + bd.$

所以正确答案是 A。

Note that the region is a rectangle with side lengths $a - (-b) = a + b$ and $d - (-c) = c + d.$ The area is then $(a + b)(c + d) =$ $ac + ad + bc + bd.$

Thus, A is the correct answer.

2011 AMC 10A 第 9 题

答案：A

难度评级：900

解答：

其他年份的第 9 题