"What is the area? You should be able to solve this"

[Albert Chan]

I have seen the geometric solution ! (no, i did not peek)

Since all points A=(0,2), B=(2,0), C=(4,2), D=(2,4) is the mid-point of square side,
Join them all, and it is still a square (no coordinates needed, but I can't draw with words)

Within this smaller square, the opposite triangles must sum to half of square.
(same base, 2 height sum to base, thus 2 triangles sum to base*base/2)

so, back to big square ...

opposite quadrilaterals also sum the same, to half of big square.

20 cm^2 + sx = 16 cm^2 + 32 cm^2

-> sx = 28 cm^2