Question

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
of the square PQRS.By PythograsTheorem

Answer 1

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.

Answer 2

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