Question

Area of trapezium?

Answer 1

`30`

Explanation:

A great way to remember the area of a trapezium is using this rhyme, sung to the tune of 'Pop goes the Weasel'.
'Add together the parallel sides,
Times half the distance between them,
That's the way the area goes,
Of a trapezium.'

For this trapezium, we would add the parallel sides, so `6+9=15`.

The next step is to find the length DE. As triangles CDB and CEA have the same ratios, we can use this to calculate DE. The ratio of side to bottom in CDB is `8/6`. If we times this by our bottom length of `9`, we end up with `12`. This is the length of CE.
All that is left to find DE, is to take CD away from CE. Therefore, `12-8=4`.

Then we can continue with our trapezium song. Times half the distance between them, so `15*(4/2)=15*2=30`.
Therefore, our area of ABDE is `30`.

Answer 2

`30 sq.unit`

Explanation:

Area of the Trapezium ABDC

`="the Area of right-"DeltaACE"--that of right-"DeltaBCD"`

`=1/2*AE*CE-1/2*BD*CD..........(ast)`

But, `DeltaACE` is similar to `DeltaBCD,` giving,

`(AE)/(BD)=(CE)/(CD) rArr 9/6=(CE)/8`

`:. CE=12`

Therefore, by `(ast)`, the Reqd. Area,

`=1/2*9*12-1/2*6*8=54-24=30 sq.unit`

Otherwise, knowing the Formula,

`"The Area of the Trapezium="1/2*DE*(AE+BD)`

`=1/2*(12-8)(9+6)=30 sq.unit`