Question

PQRS is a parallelogram. X and Y are midpoints of sides PQ and RS respectively. W and Z are points of intersection of SX and PY and XR and YQ respectively. show that ar(YWZ)=ar(XWZ) please answer .......

Answer 1

Given   PQRS is a parallelogram.X and Y are mid points of  PQ and SR respectively and PS∥XY∥QR
Construction  Draw SM⊥PQ 

Now  area∥gmXQRYarea ∥gmPQRS= XQ×SMPQ×SM=12PQPQ=12   
   ∴   area  ∥gm X Q R Y   =  12 a r e a   ∥ g m P Q R S   =  12 × 24   c m 2 = 12   c m 2 

N o w  area∥gmXQYSarea∥gmXQRY = XQ×SMXQ×SM = 1 
∴ a r e a ∥ g m   X Q Y S   =   a r e a ∥ g m X Q R Y   =   12   c m 2 


Note:-  Height is same for all parallelograms as they are between the same parallel lines.