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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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