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Nazma's sister also has a trapeziumshaped plot. Divide it into three parts as shown (Fig 11.4). Show that the area of a trapezium

1    Nazma’s sister also has a trapezium-shaped plot. Divide it into three parts as shown (Fig 11.4). Show that the area of a trapezium 

        WXYZ=h\frac{(a+b)}{2}.

 

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Area of trapezium WXYZ = Area of triangle with base 'c' + area of rectangle + area of triangle with base'd'

                                         =(\frac{1}{2}\times c\times h)+(b\times h)+\left ( \frac{1}{2}\times d\times h \right )

Taking 'h' common, we get

                                          =(\frac{c}{2}+b+\frac{d}{2})h

                                         =h(\frac{c+d}{2}+b)

  Replacing   c+d =a-b          

                                        =h(\frac{a-b}{2}+b)

                                        =h(\frac{a+b}{2})

Hence proved that the area of a trapezium 

WXYZ=h\frac{(a+b)}{2}..

          

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