quadrilateral in a square

Chris Pritchard sets some interesting tasks in Mathematics in School Vol. 43 No.2
that involve having vertices of a quadrilateral drawn so that they divide each side in the ratio a : b (or b : a)
I have very slightly adapted his fine work

establish geometrically and also algebraically that the red quadrilateral is half of the surrounding square

show that the two red quadrilaterals sum to the initial square

try to do this geometrically and then also algebraically