2026 AMC 8 第 13 题

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

小提示：

观察阴影正方形的一条边。

Look at one side of the shaded square

大提示：

这条边对应水平移动

3

个单位、竖直移动

1

个单位。

That side moves

3

units horizontally and

1

unit vertically

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

.