In the $xyz$ coordinate system, a triangle has vertices at $(1,2,3), (-4,-5,-6),$ and $(7,8,9)$ .

What is the area of the triangle (to 1 decimal place)?

The answer is 14.7.

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See @William Whitehouse for a nice solution using Heron's formula. Another easy way to do it is to construct two vectors using the three vertices, and then calculate the triangle area as half the magnitude of the cross product of those two vectors.

$\vec{v_1} = (-4,-5,-6) - (1,2,3) = (-5,-7,-9) \\ \vec{v_2} = (7,8,9) - (1,2,3) = (6,6,6) \\ \vec{v_1} \times \vec{v_2} = (12,-24,12) \\ \frac{1}{2} |\vec{v_1} \times \vec{v_2}| \approx 14.7$