Smaller square

Let the points A, B, C and D are midpoints of the sides of the square PQRS. If the area of PQRS is 100 sq cm, what is the area of the smaller square ABCD?

Correct answer:

S2 =  50 cm2

Step-by-step explanation:

S1=100 cm2  S1 = a2 a=S1=100=10 cm  (a/2)2+(a/2)2 = b2  b=2 (a/2)2=2 (10/2)2=5 2 cm7.0711 cm  S2=b2=7.07112=50 cm2

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