AMC10 2018 A

AMC10 2018 A · Q9

AMC10 2018 A · Q9. It mainly tests Similarity, Area & perimeter.

All of the triangles in the diagram below are similar to isosceles triangle $ABC$, in which $AB = AC$. Each of the 7 smallest triangles has area 1, and $\triangle ABC$ has area 40. What is the area of trapezoid $DBCE$?

图中所有三角形都与等腰三角形 $\triangle ABC$（$AB = AC$）相似。最小的 7 个三角形每个面积为 1，$\triangle ABC$ 面积为 40。梯形 $DBCE$ 的面积是多少？

(A) 16 16

(B) 18 18

(D) 22 22

(E) 24 24

Answer

Correct choice: (E)

正确答案：（E）

Solution

Answer (E): The length of the base $\overline{DE}$ of $\triangle ADE$ is 4 times the length of the base of a small triangle, so the area of $\triangle ADE$ is $4^2 \cdot 1 = 16$. Therefore the area of $DBCE$ is the area of $\triangle ABC$ minus the area of $\triangle ADE$, which is $40 - 16 = 24$.

答案（E）：$\triangle ADE$ 的底边 $\overline{DE}$ 的长度是一个小三角形底边长度的 4 倍，因此 $\triangle ADE$ 的面积为 $4^2 \cdot 1 = 16$。所以四边形 $DBCE$ 的面积等于 $\triangle ABC$ 的面积减去 $\triangle ADE$ 的面积，即 $40 - 16 = 24$。

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