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Area of a Triangle Given Its Vertices

Find the area...

Question

Find the area of $Δ$ PQR whose vertices are $P (2, 1), Q (3, 4)$ and $R (5, 2)$ .

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Solution

$P (2, 1) Q (3, 4) R (5, 2)$
Area of triangle $= \frac{1}{2} | x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) |$
$= \frac{1}{2} | 2 (4 - 2) + 3 (2 - 1) + 5 (1 - 4) |$
$= \frac{1}{2} | 2 (2) + 3 (1) + 5 (- 3) |$
$= \frac{1}{2} | | 4 + 3 - 15 | = \frac{8}{2} = 4 s q . u n i t s$

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