A solid red plastic cube, volume 1 cm, is painted white on its outside. The cube is cut by a plane passing through the mid-point of various edges, as shown.
What, in cm, is the total red area exposed by the cut?
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\frac{3\sqrt{3}}{2}
2
\frac{9\sqrt{2}}{5}
3
\frac{3(\sqrt{3} + \sqrt{2})}{4}
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Senior Mathematical Challenge 2006 (2006)
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