AMC8 2011

AMC8 2011 · Q7

AMC8 2011 · Q7. It mainly tests Fractions, Area & perimeter.

Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles and is partially shaded. What percent of the total area is partially shaded?

以下四个全等的大正方形每个都被细分为全等的三角形或矩形的组合，并部分涂阴影。部分涂阴影的区域占总面积的百分之多少？

(A) $12\frac{1}{2}$ $12\frac{1}{2}$

(B) 20 20

(D) $33\frac{1}{3}$ $33\frac{1}{3}$

(E) $37\frac{1}{2}$ $37\frac{1}{2}$

Answer

Correct choice: (C)

正确答案：（C）

Solution

Assume that the area of each square is $1$. Then, the area of the bolded region in the top left square is $\dfrac{1}{4}$. The area of the top right bolded region is $\dfrac{1}{8}$. The area of the bottom left bolded region is $\dfrac{3}{8}$. And the area of the bottom right bolded region is $\dfrac{1}{4}$. Add the four fractions: $\dfrac{1}{4} + \dfrac{1}{8} + \dfrac{3}{8} + \dfrac{1}{4} = 1$. The four squares together have an area of $4$, so the percentage bolded is $\dfrac{1}{4} \cdot 100 = \boxed{\textbf{(C)}\ 25}$.

假设每个正方形的面积为$1$。左上正方形粗体区域面积为$\dfrac{1}{4}$。右上粗体区域面积为$\dfrac{1}{8}$。左下粗体区域面积为$\dfrac{3}{8}$。右下粗体区域面积为$\dfrac{1}{4}$。四个分数相加：$\dfrac{1}{4} + \dfrac{1}{8} + \dfrac{3}{8} + \dfrac{1}{4} = 1$。四个正方形总面积为$4$，因此涂阴影的百分比为$\dfrac{1}{4} \cdot 100 = \boxed{\textbf{(C)}\ 25}$。

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