ABCD is a quadrilateral in which AB || DC, and E and F are the mid points of the diagonals AC and BD, respectively. If AB = 60 cm, BC = 65 cm, DC = 18 cm, and AD = 10 cm, then what is the length (in cm) of EF?
21
ABCD is a trapezium with \(AB \parallel DC\), where E and F are the midpoints of diagonals AC and BD respectively.
For such a trapezium, the segment joining the midpoints of the diagonals is parallel to the two parallel sides, and its length equals half the difference of the lengths of the parallel sides.
This gives \(EF = \frac{AB - DC}{2}\).
Substituting the given values: \(EF = \frac{60 - 18}{2} = \frac{42}{2} = 21\) cm.
Hence, the length of EF is 21 cm.
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