AMC8 2005

AMC8 2005 · Q13

AMC8 2005 · Q13. It mainly tests Area & perimeter, Coordinate geometry.

The area of polygon ABCDEF is 52 with AB = 8, BC = 9 and FA = 5. What is DE + EF?

多边形 ABCDEF 的面积为 52，AB = 8，BC = 9，FA = 5。DE + EF 是多少？

(A) 7 7

(B) 8 8

(D) 10 10

(E) 11 11

Answer

Correct choice: (C)

正确答案：（C）

Solution

Rectangle $ABCG$ has area $8 \times 9 = 72$, so rectangle $FEDG$ has area $72 - 52 = 20$. The length of $FG$ equals $DE = 9 - 5 = 4$, so the length of $EF$ is $\frac{20}{4} = 5$. Therefore, $DE + EF = 4 + 5 = 9$.

矩形 $ABCG$ 的面积为 $8 \times 9 = 72$，所以矩形 $FEDG$ 的面积为 $72 - 52 = 20$。$FG$ 的长度等于 $DE = 9 - 5 = 4$，因此 $EF$ 的长度为 $\frac{20}{4} = 5$。所以，$DE + EF = 4 + 5 = 9$。

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