Problem 06 The plane section ABCD shown in the figure is cut from a cube of edge a. Find the area of the section if D and C are each at the midpoint of an edge.
Solution 06
$x^2 = \frac{5}{4}a^2$
$x = \frac{1}{2}\sqrt{5} \, a$
Area of section ABCD $A_{ABCD} = ax$
$A_{ABCD} = a(\frac{1}{2}\sqrt{5} \, a)$
$A_{ABCD} = \frac{1}{2}\sqrt{5} \, a^2$ answer
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