Arddhendu Shekhar Dash. How we derive Area of a Trapezium. How we are teaching Trapezium.

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Presentation transcript:

Arddhendu Shekhar Dash

How we derive Area of a Trapezium. How we are teaching Trapezium.

What should we Aim at ……….. Show relations between different but related shape to understand area of trapezium. Trapezium is related to parallelogram in one way as in both the cases one opposites sides are parallel. Their mutual relations can be explored in understanding the area of trapezium.

A B DC  Consider a Trapezium ABCD.  Suppose AB=a units., CD = b units & height XY= h units. a units b units  Draw a parallel line EF such that is passes through the mid point of height XY. E F X Y h units

A B DC  Now divide the trapezium from the line EF so we get two trapezium ABFE & EFCD. a units b units E F X Y h units DC b units E F

A B DC a units b units E F X Y h units  Now turn the upper trapezium EFCD vertically.

A B DC a units b units E F X Y h units D C b units EF  Join the upper trapezium EFCD in the side of the lower trapezium ABFE

A B DC a units b units E F X Y h units P b units  Now it forms a parallelogram APQE.  AP = AB + BP = (a+b) units & heights = XY/2 = h/2 units Q h/2 units

A B DC a units b units E F X Y h units P b units  Area of the trapezium ABCD = Area of the parallelogram APQE = h/2 (a+b) sq. units. Q h/2 units