52 cm
(a) none
ABCD is a trapezium in which AB || CD, as shown. The area of the
trapezium is
(a) 1350 cm? (b) 1612 cm (c) 1620 cm
28 cm
28 CM
(d) none
E
78 cm
Answers
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8th
Maths
Mensuration
Area of Trapezium
ABCD is a trapezium in whic...
MATHS
ABCD is a trapezium in which AB∥CD; 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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ANSWER
Draw CE∥DA and CF⊥AB.
Therefore, ADCE is a parallelogram having AE∥CD and CE∥DA.
⇒AD=CE=39cm,DC=AE=30cm and BE=75−30=45cm
In △BCE, by heron's formula we have
a=39cm,b=45cm and c=42cm
⇒s=
2
a+b+c
=
2
39+42+45
=63cm
∴ Area of ΔBEC=
s(s−a)(s−b)(s−c)
=
63(63−39)(63−42)(63−45)
cm
2
=
63×24×21×18
cm
2
=756cm
2
Also, Area of ΔBEC=
2
1
×base×height
⇒
2
1
×45×h=756cm
2
⇒h=33.6cm
So, Area of trapezium:-
=
2
1
×(AB+CD)×height
=
2
1
×(75+30)×33.6=1764cm
2
solution