Question

if p,a,r,k are the midpoints of the sides of the parallelogram NICE. show that ar(PARK)=½ar(NICE)​

Answer 1

Step-by-step explanation:

REF.Image.

In △ADC, by mid point

theorem, SR∥AC,SR=

2

1

(AC)

Similarly PQ∥AC,PQ=

2

1

(AC)

⇒PQ∥RS, similarly PS∥QR

⇒ opposite sides parallel

⇒PQRS is a parallelogram

As △ALS∼△AOD (AA similarity)

⇒

OD

SL

=

AD

AS

=

2

1

⇒ Area of rectangle SL×R

=SL×L×=

2

1

(OD)(

2

AC

)

{LX×=SR=

2

AC

}=

2

1

(ar△ACD)

⇒ Area of PQRS=

2

1

(arACD)

+

2

1

(arACB)=

2

1

(arABCD)