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Question

The parallel sides of a trapezium are 23 cm and 13 cm. Its non-parallel sides are 10 cm each. Find the area of trapezium.

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Solution

Given AB=13 cm,CD=23 cm,AC=BD=10 cm each
construction Draw APCD & BQCD
Formulae:(i)Area of a trapezium =12×15 cm of parallel sides)×(perpendicular distance between then)
(ii) Pythagoras theorem
In quad ABPQ
ABPQ
APBQ & AP=BQ{parallel lines} - (1)
In APC & BQD
APC=BQD=90o {construction}
AC=BD=10 cm= given
AP=BQ {from (1)}
By RHS rule of congruence, APCBQD
Now let PC=QD=x
2x+PQ=CD
2x=2313=10 cmx=5 cm
In APC & BQD
AP & BQ=(10)2(5)2=53 cm {Pythagoras Theorem}
Now area of Trapezium ABCD
=12×(AB+CD)×AP
=12×(13+23)×53 cm2
=12×36×53 cm2
=903 cm2



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