Find the area of the quadrilaterals, the coordinates of whose vertices are $(- 3, 2), (5, 4), (7, - 6)$ and $(- 5, - 4)$

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Solution

Area $= \frac{1}{2} ∣ ∣ ∣ \begin{matrix} x_{1} & x_{2} & x_{3} & x_{4} y_{1} & y_{2} & y_{3} & y_{4} \end{matrix} ∣ ∣ ∣$
$= \frac{1}{2} | x_{1} + y_{2} + x_{2} y_{3} + x_{3} y_{4} + x_{4} y_{1} - x_{3} y_{1} - x_{3} y_{2} - x_{4} y_{3} - x_{1} y_{4} |$
$= \frac{1}{2} | - 12 - 30 - 28 - 10 - 10 - 28 - 30 - 12 |$
$= 80 s q, x t s$

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Find the area of a quadrilateral ABCD, the coordinates of whose varities are A (-3, 2), B (5, 4), C (7, -6) and (-5, -4).

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