2014 AMC 8 第 6 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
6.
六个长方形的共同底宽都是 ，长度分别为 ，，，， 和 。这六个长方形面积之和是多少？
Six rectangles each with a common base width of have lengths of and What is the sum of the areas of the six rectangles?
小提示：
每个长方形面积等于 乘以其列出的长度
Each rectangle has area times its listed length.
大提示：
先把长度相加，再乘以
Add the lengths first, then multiply by .
解答：
每个长方形面积是 乘对应长度。可以先把共同因子 提出来，只需求长度之和，即 。
因此面积之和为 。
所以正确答案是 D。
To find the area of each rectangle we multiply by their respective lengths. This means that we can factor out the and we are left with the sum of the lengths. Adding together the lengths, we get
Therefore, the sum of the areas is
Thus, D is the correct answer.
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