1.

Prove that the area of a trapezium is half the sum of the parallel sides multiplied by thedistance between them.1

Answer»

Let ABCD be a parallelogram, and BD be the diagonal forming two triangles ABD and BCD.Let DE be the height of trapezium ABCD.Area of trapezium ABCD=Area of tr. ABD+Area of tr. BCDSo, area of tr. ABD= 1/2×base×height=1/2×AB×DE..(i)

Similarly, area of tr. BCD=1/2×DC×DE ..(ii) [Both triangles will have the same height as they lie between the same parallel lines]Now, area of trap.= sum of eq(i) and (ii)So, (1/2×AB×DE) + (1/2×DC×DE)1/2×DE(AB+DC)Hence, proved



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