Question

If A (-4, 8), B(-3, -4), C(0, -5) and (5, 6) are vertices of a quadrilateral ABCD. Find it's area

Answer 1

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Answer:

Ar.(ABC),

$= \frac{1}{2} |( - 4)( - 4 - 8) + ( - 3)( - 5 - 8) + (0)( - 4 + 4)| \\ \\ = \frac{1}{2} ( - 4)( - 12) - 3( - 13) + 0 \\ \\ = \frac{1}{2} \times ( - 16) + 39 \\ \\ = \frac{1}{2} \times - 23 \\ \\ = 11.5 \: cm {}^{3}$

Ar.(AOD),

$= \frac{1}{2} |( - 4)(6 + 5) + (5)( - 5 - 8) + 0| \\ \\ = \frac{1}{2} \times ( - 4)(11) + 5( - 13) \\ \\ = \frac{1}{2} \times ( - 44 - 65) \\ \\ = \frac{109}{2} \\ \\ = 76.5 \: cm {}^{3}$

Area of quadrilateral = Ar.(ABC) + Ar.(AOD) = 11.5 + 76.5

= 88 cm.

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