Question

Find the area of a trapezium whose parallel sides are 11 m and 25 m long, and the nonparallel sides are 15 m and 13 m long.

Answer 1

 

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`