Question

D 6 cm In Fig. 21.8. ABCD is a trapezium in which AB || CD and CE 1 AB. Also AB = 10 cm, CD = 6 cm and/ BC = 5 cm. Find the area of the trapezium. 5 cm 4 cm F 6 cm Fig. 21.8​

Answer 1

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

Step-by-step explanation:

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