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If $$D(3, -1)$$, $$E(2, 6)$$ and $$F(-5, 7)$$ are the mid points of the sides of $$\triangle ABC$$ then the area of $$\triangle ABC$$ is
Area of $$\triangle DEF = \frac{1}{2}\left|3(6 - 7) + 2(7 + 1) + (-5)(-1 - 6)\right| = \frac{1}{2}\left|-3 + 16 + 35\right| = 24$$. The triangle formed by joining the mid points has one-fourth the area of the original triangle, so area of $$\triangle ABC = 4 \times 24 = 96$$.
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