AMC8 2026

AMC8 2026 · Q6

AMC8 2026 · Q6. It mainly tests Area & perimeter.

Peter lives near a rectangular field that is filled with blackberry bushes. The field is 10 meters long and 8 meters wide, and Peter can reach any blackberries that are within 1 meter of an edge of the field. The portion of the field he can reach is shaded in the figure below. What fraction of the area of the field can Peter reach?

彼得住在一个长方形的田地附近，田地里长满了黑莓灌木。田地长10米，宽8米，彼得可以够得着离田地边缘1米以内的任何黑莓。田地中彼得能够够到的部分在下面的图中阴影部分所示。彼得能够够到的田地面积占田地总面积的几分之几？

(A) \frac{1}{6} \frac{1}{6}

(B) \frac{1}{4} \frac{1}{4}

(D) \frac{3}{8} \frac{3}{8}

(E) \frac{2}{5} \frac{2}{5}

Answer

Correct choice: (E)

正确答案：（E）

Solution

We can calculate this reachable area to be $\text{Total area} - \text{Unreachable area}$. The total area is $8 \cdot 10 = 80$, and the unreachable area is $(8-2)(10-2) = 6\cdot 8 = 48$. Thus, our answer is $\frac{80-48}{80} = \frac{32}{80} = \boxed{ \textbf{(E) } \frac{2}{5} }$.

我们可以计算彼得能够够到的面积为$\text{总面积} - \text{不可够到的面积}$。总面积是$8 \cdot 10 = 80$，不可够到的面积是$(8-2)(10-2) = 6 \cdot 8 = 48$。因此，答案是$\frac{80-48}{80} = \frac{32}{80} = \boxed{ \textbf{(E) } \frac{2}{5} }$。

Topics

GE.007 Area & perimeter