Square ABCD and trapezoid BEFC do not lie in the same plane. Find the length of the base EF if AB = 8

univerkov | August 8, 2021 | education

Square ABCD and trapezoid BEFC do not lie in the same plane. Find the length of the base EF if AB = 8, and the distance between the midpoints of the segments AE and FD is 5 cm.

ABCD – a square with opposite sides parallel, then BC || AD.

In the BCFE trapezoid, the bases of BC and EF are also parallel.

Then EF is parallel to AD, and therefore the quadrilateral ADEF is a trapezoid, in which AD = 8 cm, as the length of the side of the square, and KM, by condition, has its middle line and is equal to 5 cm.

Then, according to the formula for the middle line of the trapezoid, KM = (AD + EF) / 2.

EF = 2 * KM – AD = 2 * 5 – 8 = 10 – 8 = 2 cm.

Answer: The length of EF is 2 cm.

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