Question

The midpoints of the sides of a parallelogram are joined to form a small parallelogram. If the area of the small parallelogram is 20cm^2, then the area of the original parallelogram is:
Please explain.

Answer 1

is this question from base coaching assignment? the answer is 40 cm^2

Let P,Q,R,S be respectively the midpoints of the sides AB, BC, CD, DA of quad. ABCD and let PQRS be formed by joining the midpoints.

Now, join AC.

In triangle ABC, P and Q are midpoints of AB and BC respectively.

So by mid point theorem,

PQ ll AC and PQ = 1/2 AC.

Now,

In triangle DAC, S and R are midpoints of AD and DC respectively.

Therefore, SR ll AC and SR = 1/2 AC.

Thus, PQ ll SR and PQ = SR.

Hence, PQRS is a ll gm.

Now, join AR which divides triangle ACD into two equal area.

∴ar ( AED ) = 1/2 ar ( ACD )  .. ( 1 )

Median RS divides triangle ARD into two triangle of equal area.

Hence, ar ( DSR ) = 1/2 ( ARD )  .. ( 2 )

From ( 1 ) and ( 2 ), we get : ar ( DSR ) = 1/4 ( ACD ).

Similarly, ar ( BQP ) = 1/4 ( ABC ).

Now, ar ( DSR ) + ar ( BQP ) = 1/4 [ ar ( ACD ) + ar ( ABC )]

Therefore, ar ( DSR ) + ar ( BQP ) = 1/4 [ quad. ABCD] ......... ( 3 )

Similarly, ar ( CRQ ) + ar ( ASP ) = 1/4 ( quad. ABCD )  ......... ( 4 )

Adding ( 3 ) and ( 4 ) , we get

ar ( DSR ) + ar ( BQP ) + ar ( CRQ ) + ar ( ASP ) = 1/2 ( quad. ABCD ) ............... ( 5 )

But, ar ( DSR ) + ar ( BQP ) + ar ( CRQ ) + ar ( ASP ) + ar ( llgm PQRS ) = ar ( quad. ABCD ) .... ( 6 )

Subtracting ( 5 ) from ( 6 ) , we get

ar ( llgm PQRS ) = 1/2 ar ( quad. ABCD ).

Mark it as brainlist

Thnx

Answer 2

excus e me ma m plevase ans wer allb my questi on whi ch I a sk n ow pleas e pl ease