In rectangular parallelepiped ABCDA1B1C1D1 edge BC = 4, edge, edge BB1 = 2. Point K is the midpoint of edge CC1. Find the area of the section through points B1, A1 and K.
From point K, the middle of CC1, construct a segment KN parallel to CD. Section А1В1СD is a rectangle, then КН = СD = AB = 2 * √5 cm.
From point K we construct a segment KM parallel to BC, then KM = BC = 4 cm.
Since point K is the middle of CC1, then KC1 = MB1 = CC1 / 2 = 4/2 = 2 cm.
In a right-angled triangle КМВ1, according to the Pythagorean theorem, КВ1 ^ 2 = КМ ^ 2 + MB1 ^ 2 = 16 + 4 = 20. КВ1 = 2 * √5 cm.
Then Ssec = КВ1 * КН = 2 * √5 * 2 * √5 = 20 cm2.
Answer: The cross-sectional area is 20 cm2.
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