AMC8 2009

AMC8 2009 · Q7

AMC8 2009 · Q7. It mainly tests Area & perimeter.

The triangular plot of land ACD lies between Aspen Road, Brown Road and a railroad. Main Street runs east and west, and the railroad runs north and south. The numbers in the diagram indicate distances in miles. The width of the railroad track can be ignored. How many square miles are in the plot of land ACD?

三角形地块ACD位于Aspen路、Brown路和一条铁路之间。Main Street呈东西走向，铁路呈南北走向。图中的数字表示英里的距离。铁路轨道的宽度可以忽略不计。地块ACD有多少平方英里？

(A) 2 2

(B) 3 3

(D) 6 6

(E) 9 9

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): The area of $\triangle ABC$ is $\frac{1}{2}(3)(3)=\frac{9}{2}$ square miles. The area of $\triangle ABD=\frac{1}{2}(3)(6)=9$ square miles. The shaded area is the area of $\triangle ABD$ minus the area of $\triangle ABC$, which is $9-\frac{9}{2}=\frac{9}{2}=4.5$ square miles. OR The base $\overline{CD}$ of $\triangle ACD$ is 3 miles. The altitude $\overline{AB}$ of $\triangle ACD$ is 3 miles. The area of $\triangle ACD$ is $\frac{1}{2}\cdot 3\cdot 3=\frac{9}{2}=4.5$ squares miles.

答案（C）：$\triangle ABC$ 的面积是 $\frac{1}{2}(3)(3)=\frac{9}{2}$ 平方英里。$\triangle ABD$ 的面积是 $\frac{1}{2}(3)(6)=9$ 平方英里。阴影部分面积等于 $\triangle ABD$ 的面积减去 $\triangle ABC$ 的面积，即 $9-\frac{9}{2}=\frac{9}{2}=4.5$ 平方英里。或者 $\triangle ACD$ 的底边 $\overline{CD}$ 为 3 英里，高 $\overline{AB}$ 为 3 英里。$\triangle ACD$ 的面积为 $\frac{1}{2}\cdot 3\cdot 3=\frac{9}{2}=4.5$ 平方英里。

Topics

GE.007 Area & perimeter