Question

The area of a square is 100 cm2. Find the area of the square formed by joining the midpoints
of the sides of the given square.
answer fast ​

Answer 1

Step-by-step explanation:

⇒  AB=BC=CD=AD=92cm             [ Given ]

⇒  AP=21AB                  [ P is midpoint of AB ]

⇒  AP=21×92=292cm

∴  AP=AS=292

⇒  ∠PAS=90o              [ Angle of square is 90o ]

In right angled △PAS

⇒  (PS)2=(AP)2+(AS)2              [ By Pythagoras theorem ]

⇒  (PS)2=(292)2+(292)2

⇒  (PS)2=4162