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?

Video solution:

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Written solution:

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 $10$.