Question

the distance between parallel sides of a Trapezium is 12 cm and the distance between midpoints of other side is 18 cm find the area of trapezium

Answer 1

your answer is 126 cmsq.....

Answer 2

Here , Diagonal BD intersect line EF at " O " .

And we assume O' is mid point of line BD .

In ∆ ABD , E and O' are mid points of AD and BD respectively , So from converse of mid point theorem we get

AB | | EO' ---- ( 1 )

And

In ∆ CDB , F and O' are mid points of BC and BD respectively , So from converse of mid point theorem we get

CD | | FO' , Given ABCD is a trapezium , SO AB | | CD , Then

AB | | FO' ---- ( 2 )

From equation 1 and 2 we can say that EO'F is a straight line , So O and O' coincide.

Therefore, O is mid point of BD

From equation 2 : AB | | OF , So

EF | | AB ( hence proved )

In ∆ ABD , E and O are mid points of AD and BD respectively , So from converse

EF = AB + CD2 = Sum of parallel sides 2 --- ( 1 )

We know area of trapezium = Sum of parallel sides 2×Height

From equation ( 1 ) we get :

Area of given trapezium = EF × Height = 18 × 12 = 216 cm2 ( Ans )