AMC 8 2005 Problem 13
AMC8 2005 年第 13 题
四边形与多边形★★★☆☆
The area of polygon ABCDEF is 52 with AB=8 , BC=9 and FA=5 . What is DE+EF ?
多边形 ABCDEF 的面积是 52，其中 AB=8，BC=9，FA= 5。则 DE + EF 是多少？
- A.7
- B.8
- C.9
- D.10
- E.11
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Notice that AF + DE = BC, so DE=4. Let be the intersection of the extensions of and , which makes rectangle . The area of the polygon is the area of subtracted from the area of . Solving for the unknown, EF=5, therefore DE+EF=4+5=9.
Similar to solution 1, AF + DE = BC, so DE=4. Split the polygon into two rectangles by extending the so it intersects . Let's say the length of is equal to . We can form the equation: 5x + 9(8-x) = 52. We see that x = 5, so we can add 5 + 4 = 9. - ArjunBhumula
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