A parallelogram frame has its two diagonals along the vectors d₁ = 3 i + j - 2 k and d₂ = i - 3 j +…

Step 1. The sides. $\vec a = \dfrac{(4, -2, 2)}{2} = (2, -1, 1)$ and $\vec b = \dfrac{(2, 4, -6)}{2} = (1, 2, -3)$.

Step 2. Their lengths. $\lvert\vec a\rvert = \sqrt{6} \approx 2.45$ and $\lvert\vec b\rvert = \sqrt{14} \approx 3.74$ decimetres.

Step 3. The area from the diagonals. $\vec d_1\times\vec d_2 = (-2, -14, -10)$, with size $\sqrt{4 + 196 + 100} = \sqrt{300}$. The area is $\dfrac{\sqrt{300}}{2} = 5\sqrt{3} \approx 8.66$ square decimetres.