AMC 8 2011 Problem 7

AMC8 2011 年第 7 题

面积与周长（综合）★★☆☆☆

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

下面 4 个大的全等正方形，每个都被分成几个全等的三角形或者矩形，并且一部分用粗体表示。那么粗体部分的面积占了总面积的百分之多少？

A. $\displaystyle 12\frac{1}{2}$
B.20
C.25
D. $\displaystyle 33\frac{1}{3}$
E. $\displaystyle 37\frac{1}{2}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

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 = 25

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