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Question

ABCD is a trapezium in which ABCD; BC and AD are non-parallel sides. It is given that AB=75cm,BC=42cm,CD=30cm and AD=39cm. Find the area of the trapezium.

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Solution

Draw CEDA and CFAB.

Therefore, ADCE is a parallelogram having AECD and CEDA.

AD=CE=39cm,DC=AE=30cm and BE=7530=45cm

In BCE, by heron's formula we have

a=39cm,b=45cm and c=42cm

s=a+b+c2=39+42+452=63cm

Area of ΔBEC=s(sa)(sb)(sc)

=63(6339)(6342)(6345)cm2

=63×24×21×18cm2

=756cm2

Also, Area of ΔBEC=12×base×height

12×45×h=756cm2h=33.6cm
So, Area of trapezium:-
=12×(AB+CD)×height=12×(75+30)×33.6=1764cm2

307112_244907_ans_df1b2b1b928b4f2b848e36504bec38de.png

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