The area of a square is 16cmsq. Find the area of the square joining the mid pt. Of its side.

Question

Gv me sltn

Answer 1

let each side of the original square be 2x
so its area = 4x^2
let each side of the inner square be s
s^2 = x^2 + x^2
s = √2 x
area of inner square = (√2 x)^2 = 2x^2

so the area of the square joining the midpoints is 1/2 of the original.