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Question

Find the area of a trapezium whose parallel sides are 25 cm,13 cm and other sides are 15 cm each.

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Solution

In trapezium ABCD,parallel sides are AB and DC.

AB=25 cm,CD=13 cm and other sides are 15 cm eachi.e,AD=CB=15 cmFrom C,draw E || DA and CL AB AE=DC=13 cm and EB=ABAE=2513=12 cm Perpendicular CL bisects the base EB of the isosceles triangle CEBtherefore EL=LB=122=6 cmNow in right CLB,CB2=CL2+LB2 (Pythagoras theorem) (15)2=CL2+(6)2225=CL2+36CL2=22536=189=9×21 CL=9×21=321 cmNow, area of trapezium=12(Sum of parallel sides)×h=12(25+13)×321 cm2=12×(38)×321 cm2=19×321 cm2=5721 cm2


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