Question

5.
ABCD is a trapezium in which AB || DC, AB = 78 cm, CD = 52 cm , AD = 28 cm
and BC = 30 cm. Find the area of the trapezium.
B and CM
DA. meeting AB at L and M respectively.​

Answer 1

Step-by-step explanation:

AS AB∣∣CD and DM and

CN⊥AB⇒DM=CN=h

In △DMA,DA

2

=AM

2

+DM

2

⇒28

2

=(26−X)

2

+h

2

...(1)

In △CNB,CB

2

=CN

2

+NB

2

⇒30

2

=X

2

+H

2

...(2)

Eq

n

(1)...Eq

2

(2)−58×2=(26−x)

2

−x

2

116=x

2

−(x−26)

2

=(2x−26)26

⇒x−13=

26×2

116

=

13

29

Byeq

n

,h

2

=30

2

−

13

2

29

2

=900−

169

841

=895.02

⇒h=29.9cm

Area trapezium=

2

1

(sum of parallal sides)height=

2

1

(130)(29.2)

⇒Area=1898cm

2