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Question

Find the area of a square PQRS formed by joining the mid-points of sides of another square ABCD of side 92cm.
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Solution
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AB=BC=CD=AD=92cm [ Given ]
AP=12AB [ P is midpoint of AB ]
AP=12×92=922cm
AP=AS=922
PAS=90o [ Angle of square is 90o ]
In right angled PAS
(PS)2=(AP)2+(AS)2 [ By Pythagoras theorem ]
(PS)2=(922)2+(922)2
(PS)2=1624+1624
(PS)2=3244
(PS)2=81
PS=9cm
Area of square PQRS=(9)2=81cm2

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