Question

阴影正方形的面积与大正方形面积之比是多少？（图按比例绘制。）

What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale.)

$\dfrac{1}{6}$

$\dfrac{1}{7}$

$\dfrac{1}{8}$

$\dfrac{1}{12}$

$\dfrac{1}{16}$

答案：C

知识点：面积比面积分割

难度评级：1150

小提示：

把大正方形中的网格线延长

Extend the grid lines in the large square.

大提示：

阴影正方形由四个半单位正方形组成。

The shaded square is made from four half-unit squares.

解答：

如图，把原图延伸成一个 $4$ 乘 $4$ 的网格：

大正方形由 $16$ 个单位正方形组成。阴影正方形由四个半单位正方形组成，所以其面积为 $4\cdot\dfrac{1}{2}=2$ 。因此所求比值为 $\dfrac{2}{16}=\dfrac{1}{8}$ 。

所以正确答案是 C。

Extend the figure to a $4$ by $4$ grid as shown:

The large square consists of $16$ unit squares. The shaded square is made from four half-unit squares, so its area is $4\cdot\dfrac{1}{2}=2.$ Therefore, the required ratio is $\dfrac{2}{16}=\dfrac{1}{8}.$

Thus, the correct answer is C .

1998 AMC 8 第 13 题

答案：C

难度评级：1150

小提示：

大提示：

解答：

其他年份的第 13 题