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Area of polygons on a grid
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Learn it Shoelace formula: list the vertices in order, add the products $x_1y_2 + x_2y_3 + \dots$, subtract $y_1x_2 + y_2x_3 + \dots$, and halve the absolute value.
Example: Area of A(0, 0), B(4, 0), C(5, 3), D(1, 3).
- Down products: $0 \cdot 0 + 4 \cdot 3 + 5 \cdot 3 + 1 \cdot 0 = 27$.
- Up products: $0 \cdot 4 + 0 \cdot 5 + 3 \cdot 1 + 3 \cdot 0 = 3$.
- Area $= \frac{1}{2}|27 - 3| = 12$.
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