Answer: DE = \(4\sqrt{2}\)
All equilateral triangles are similar (each angle is \(60^\circ\), AAA test), so \(\triangle ABC \sim \triangle DEF\).
\[\frac{A(\triangle ABC)}{A(\triangle DEF)} = \frac{AB^2}{DE^2}\] \[\frac{1}{2} = \frac{4^2}{DE^2}\] \[DE^2 = 32\] \[DE = \sqrt{32} = 4\sqrt{2}\]