Q.

The area of a trapezium whose parallel sides are of lengths 40metres  and

24 metres  and whose non parallel sides are equal, each being 10 metres  is

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a

192sq.m

b

289sq.m

c

169sq.m

d

296sq.m

answer is B.

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Detailed Solution

Draw CEDA , intersects AB  at E

In quadrilateral AECD,AEDC  and CEDA

AECD  is a parallelogram

AE=DC=24cm

AD=CE=10cm

EB=ABAC

=4024=16

Area of ΔBEC

=s(sa)(sb)(sc)

Where S=16+10+102=362=18

=18×2×8×8

=9×(2×2)×(8×8)

=(3×3)×(2×2)×(8×8)

=3×2×8

=48cm2

But area of ΔBEC=12(base)×(height)

=12×16×h=48

=8×h=48

h=488=6

h=6cm

 distance between parallel sides =6cm

 Area of trapezium

=12(sumofparallelsides)×(Distancebetweenparallelsides)

=12(40+24)×6

=12(64)×6

=192cm2

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