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

D C

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

D C

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

D Cb units

E F

A B

D C

a units

b units

E F

X

Y

h units

Now turn the upper trapezium EFCD vertically.

A B

D C

a units

b units

E F

X

Y

h units

DC b units

EF

Join the upper trapezium EFCD in the side of the lower

trapezium ABFE

A B

D C

a units

b units

E F

X

Y

h units

Pb 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

D C

a units

b units

E F

X

Y

h units

Pb units

Area of the trapezium ABCD

= Area of the parallelogram APQE

= h/2 (a+b) sq. units.

Q

h/2 units