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Question
Find the area of trapezium whose parallel sides are 11 m and 25 m long, and the nonparallel sides are 15 m and 13 m long.
Solution
Draw || DE BCand DLperpendicular to AB.
The opposite sides of quadrilateral DEBC are parallel. Hence, DEBC is a parallelogram
∴`DE=BC=13m`
Also,
`AE=(AB-EB)=(AB-DC)=(25-11)=14m`
For Δ DAF:
Let:
`AE=a=14m`
`DE=b=13m`
`DA=c=15m`
Thus, we have:
`s=(a+b+c)/2`
`s=(14+13+15)/2=21m`
Area of ΔDAE=`1/2xxAExxDL`
⇒` 84=1/2xx14xxDL`
⇒`(84xx2)/14=DL`
⇒`DL=12m`
Area of trapezium=`1/2xx"(Sum of parallel sides)"xx"(Distance between them)"`
=`1/2xx(11+25)xx12`
=`1/2xx36xx12`
=`216m^2`
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