Question

图中由 $1 \times 1$ 的单位正方形铺成，相邻两行之间水平错开半个单位。阴影正方形的每个顶点都是某个单位正方形的顶点。阴影正方形的面积是多少？

The figure below shows a tiling of $1 \times 1$ unit squares. Each row of unit squares is shifted horizontally by half a unit relative to the row above it. A shaded square is drawn on top of the tiling. Each vertex of the shaded square is a vertex of one of the unit squares. In square units, what is the area of the shaded square?

$10$

$\dfrac{21}{2}$

$\dfrac{32}{3}$

$11$

$\dfrac{34}{3}$

答案：A

知识点：勾股定理正方形（几何）

难度评级：1330

视频讲解：

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文字解答：

阴影正方形的一条边可以看作直角三角形的斜边，其中水平距离为 $3$ ，竖直距离为 $1$ 。因此边长的平方为 $3^2+1^2=10$ 。正方形面积等于边长的平方，所以面积为 $10$ 。

One side of the shaded square goes $3$ unit widths horizontally and $1$ unit vertically in the grid. Its length squared is therefore $3^2+1^2=10$ . The area of a square equals its side length squared, so the shaded area is $10$ .

2026 AMC 8 第 13 题

答案：A

难度评级：1330

视频讲解：

文字解答：

其他年份的第 13 题