PQRS is a square E is the mid-point of QR and F is the mid-point of RS The - Maths - Quadrilaterals

Question

P Q R S   i s   a   s q u a r e   E   i s
  t h e   m i d - p o i n t   o f   Q R  
a n d   F   i s   t h e   m i d - p o i n t
  o f   R S   T h e   r a t i o   o f
  t h e   a r e a   o f   ∆ P E F  
t o   t h e   a r e a   o f   s q u a r e
  P Q R S   i s

Shruti Tyagi · Accepted Answer

Dear student,
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Let a be the sides of squareArea of square=side×side=a×a=a2Area of ∆PSF=12×a2×a=a24Area of ∆PQE=12×a×a2=a24Area of ∆REF=12×a2×a2=a28Area of ∆PEF=Area of square-Area of ∆PSF+Area of ∆PQE+Area of ∆REF=a2-a24+a24+a28=a2-2a2+2a2+a28=a2-5a28=8a2-5a22=3a28⇒Area of ∆PEF=3a28Now, Area of ∆PEFArea of square PQRS=3a28a2=38Thus the ratio of Area of ∆PEF to Area of square PQRS=3:8

Regards

P Q R S i s a s q u a r e . E i s t h e m i d - p o i n t o f Q R a n d F i s t h e m i d - p o i n t o f R S . T h e r a t i o o f t h e a r e a o f ∆ P E F t o t h e a r e a o f s q u a r e P Q R S i s

$P Q R S i s a s q u a r e . E i s t h e m i d - p o i n t o f Q R a n d F i s t h e m i d - p o i n t o f R S . T h e r a t i o o f t h e a r e a o f ∆ P E F t o t h e a r e a o f s q u a r e P Q R S i s$