Question

7. In the adjoining figure, ABCD is a trapezium in which AB || DC; AB = 7 cm; AD = BC = 5 cm and the distance between AB and DC is 4 cm Find the length of DC and hence, find the area of trap. ABCD​

Answer 1

Step-by-step explanation:

Consider △ALD

Based on the Pythagoras theorem

AL

2

+DL

2

=AD

2

By substituting the values

4

2

+DL

2

=5

2

So we get

DL

2

=5

2

−4

2

DL

2

=25−16

By subtraction

DL

2

=9

By taking square root

DL=

9

so we get

DL=3 cm

We know that, DL=MC…( Sides of Triangle with equal length of two other sides )

So we get

MC=3 cm

From the figure, we know that LM=AB=7cm

So we know that CD=DL+LM+MC

By substituting the values

CD=3+7+3

By addition

CD=13cm

Area of Trapezium ABCD=

2

1

( sum of parallel sides \times distance between them )

So we get

Area of Trapezium ABCD=

2

1

×(CD+AB)×AL

By substituting the values

Area of Trapezium ABCD=

2

1

×(13+7)×4

On further calculation

Area of trapezium ABCD=20×2

By multiplication

Area of trapezium ABCD=40 cm

2

Therefore, length of DC=13cm and area of trapezium ABCD=40 cm

2

.

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