Geometrical Puzzle - Solution

What was the puzzle?

Let's draw a line from each of vertex to the point at which all 4 regions intersect. This divides the given area into 2 triangles as shown below.

Obviously, here A and A' have equal area as they both share same base QS and height OT. Similarly, the areas of B & B', areas of C & C' and areas of D & D' must be equal. 

Rewriting, A = A', B = B', C = C' and D = D'.

 
Now rewriting respective areas,

It's clear that,

A + B = 32

C + D = 16

Adding above 2 equations gives, 

A + B + C + D = 32 + 16 = 48

But from figure, B + C = 20,

A + 20 + D = 48

A + D = 28.

That's the area of the shaded region which is equal to 28 Sq.cm