AMC8 2014

AMC8 2014 · Q6

AMC8 2014 · Q6. It mainly tests Area & perimeter, Patterns & sequences (misc).

Six rectangles each with a common base width of $2$ have lengths of $1, 4, 9, 16, 25$, and $36$. What is the sum of the areas of the six rectangles?

六个矩形，每个矩形的底边宽度为 $2$，长度分别为 $1, 4, 9, 16, 25$ 和 $36$。这六个矩形的面积和是多少？

(A) 91 91

(B) 93 93

(D) 182 182

(E) 202 202

Answer

Correct choice: (D)

正确答案：（D）

Solution

The sum of the areas is equal to $2\cdot1+2\cdot4+2\cdot9+2\cdot16+2\cdot25+2\cdot36$. This is equal to $2(1+4+9+16+25+36)$, which is equal to $2\cdot91$. This is equal to our final answer of $\boxed{\textbf{(D)}~182}$.

面积和等于 $2 \cdot 1 + 2 \cdot 4 + 2 \cdot 9 + 2 \cdot 16 + 2 \cdot 25 + 2 \cdot 36$。这可以写成 $2(1 + 4 + 9 + 16 + 25 + 36)$，等于 $2 \cdot 91$。最后的答案是 $\boxed{\textbf{(D)}~182}$。

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