Question

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​

Answer 1

Step-by-step explanation:

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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