Problem 10 Pass a plane through a cube so that the section formed will be a regular hexagon. If the edge of the cube is 2 units, find the area of this section.
Solution 10
$x^2 = 2 \, \text{ unit}^2$
Area of hexagon $A = 6(\frac{1}{2}x^2 \, \sin 60^\circ)$
$A = 6[ \, \frac{1}{2}(2) \, \sin 60^\circ \,]$
$A = 3\sqrt{3} \, \text{ unit}^2$ answer
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