The outer figure is a square and the lines bisect the opposite sides.

What is the area of the central white square?

Let the side length of the white square be $x$.

By Pythagoras’ theorem,

$x^2+(x+x)^2=(5+5)^2$
$x^2+(2x)^2=(10)^2$
$x^2+4x^2=100$
$5x^2=100$
$x^2=20$

$\therefore\;\; A =x^2=20$