If P (-5, -3), Q (-4, -6) , R (2, -3) and S (1, 2) are the vertices of a quadrilateral PQRS, find its area.

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Solution

Area of triangle is given by $\frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$

Area of quadrilateral PQRS = Area of triangle PQR + Area of triangle PSR

$= \frac{1}{2} | - 5 (- 6 + 3) - 4 (- 3 + 3) + 2 (- 3 + 6) | + \frac{1}{2} | - 5 (2 + 3) + 1 (- 3 + 3) + 2 (- 3 - 2) |$

$= 10.5 + 17.5 = 28 s q . u n i t s$

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