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The area of square ABCD is 144 sq cm.let PQRS be the square obtained by joining the mid-points of the sides of the square ABCD.find the perimeter and area

As ABCD is a square ⇒a² = 144 ⇒a =√144 = 12 mid points will divide the side into half i.e. 6 as it is a square all the halfs will be 6 cm and we already know that it is 90degree so by applying pythagoras theorem hypotenuse that will be the side of the square PQRS obtained. so the side will be 6√2. so the perimeter of the square will be 4×6√2 = 24√6 and area = (6√2)² = 72.

Let side of ABCD = a Then we have a² = 144 ⇒ a =√144 = 12 cm Mid points will divide the side into half i.e. a/2=6 cm By applying Pythagoras theorem, We have
hypotenuse = side of the square PQRS = √(6²+6²)= 6√2 cm So the perimeter of PQRS is 4×6√2 = 24√2 = 33.94 cm Area of PQRS is = (6√2)² = 72 cm²