AMC8 2000

AMC8 2000 · Q25

AMC8 2000 · Q25. It mainly tests Area & perimeter.

The area of rectangle ABCD is 72. If point A and the mid-points of $\overline{BC}$ and $\overline{CD}$ are joined to form a triangle, the area of that triangle is

矩形ABCD的面积是72。若将点A与BC和CD的中点连接形成一个三角形，则该三角形的面积是

(A) 21 21

(B) 27 27

(D) 36 36

(E) 40 40

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Three right triangles lie outside $\triangle AMN$. Their areas are $\frac{1}{4}$, $\frac{1}{4}$, and $\frac{1}{8}$ for a total of $\frac{5}{8}$ of the rectangle. The area of $\triangle AMN$ is $\frac{3}{8}(72)=27$.

答案（B）：有三个直角三角形位于 $\triangle AMN$ 的外部。它们的面积分别是 $\frac{1}{4}$、$\frac{1}{4}$ 和 $\frac{1}{8}$，总共占矩形面积的 $\frac{5}{8}$。因此 $\triangle AMN$ 的面积为 $\frac{3}{8}(72)=27$。

Topics

GE.007 Area & perimeter