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.

Answer 1

permeter = 11
area =22

Answer 2

Area of square ABCD = 144 sq cm
So, side of square ABCD = 12 cm
Side of the square obtained by joining the midpoints of the ABCD = $\sqrt{ (\frac{side}{2})^2+(\frac{side}{2})^2 }$

Therefore, the side of the square PQRS = $\sqrt{ (\frac{12}{2})^2+(\frac{12}{2})^2 } = \sqrt{72} = 6 \sqrt{2}$

Area of square PQRS = $(6 \sqrt{2} )^2 = 72$ sq cm

Perimeter = 4 × $(6 \sqrt{2})$ = $24 \sqrt{2}$ cm