Question

Work out the area of the trapezium ABDE.
B
9 cm
6 cm
8 cm
→D
E

Answer 1

Area of the trapezium ABDE = 30 cm²

Explanation:

Area of a trapezium =
`(1)/(2)(b_1+b_2)h`

Here,
`b_1` and
`b_2` are the parallel sides of the trapezium

h = Distance between the parallel sides

From the picture attached,

ΔCAE and ΔCBD are the similar triangles.

So by the property of similarity their sides will be proportional.

`(AE)/(BD)= (CE)/(CD)`

`(9)/(6)=(CE)/(8)`

CE =
`(9* 8)/(6)`

CE = 12 cm

Therefore, DE = CE - CD

DE = 12 - 8 = 4 cm

Now area of trapezium ABDE =
`(1)/(2)(AE+BD)(DE)`

=
`(1)/(2)(6+9)4`

= 30 cm²

Therefore, area of the trapezium ABDE = 30 cm²