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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 $WXYZ=\frac{h}{2} \times (a+b)$.

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

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

Taking 'h' common, we get

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

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

Replacing $c+d=a-b$

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

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

Hence proved that the area of a trapezium $WXYZ=\frac{h}{2} \times (a+b)$

          

Posted by

seema garhwal

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