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 ?
A. 9
B. 10
C. $\frac{32}{3}$
D. 11
E. $\frac{34}{3}$

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Worked solution

1. 2026 AMC 8 官方解析

$S_{\text{正}} = a \times a$ ,

$a = \sqrt{1^2 + 3^2} = \sqrt{10}$ ,

$S_{\text{正}} = (\sqrt{10})^2 = 10$ .

Answer

B. 10

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