Difference between areas

Question

On the above figure: $\mbox{Area}(PQRS)=50\; cm^2$, $\mbox{Area}(ABT)=20\; cm^2$ and I am looking for the difference between the shaded areas. I have done several attempts but it seems that something is missing or is not given.I kind of figured out that it might be a case that ABCS should be expressed in another way.

Any help would be appreciated.

Answer 1

$$AREA( QRCBAP-CTS)=AREA((QRSP+BASC)-(BAT+BASC))=50-20 (cm^2) $$ You just canceled th part both the triangle and rectangle have.

Answer 2

Hint. Is the difference between the shaded areas related with the difference between the areas of the square $PQRS$ and the area of the triangle $ABT$?

Answer 3

Hint: Note that for any three numbers $a, b, c$, we have $(a-c) - (b-c) = a-b$. If I now tell you to try to assign to each of $a, b, c$ the value of specific areas in your diagram, can you see how this would help?

Answer 4

Yes I finally figured out that it is a matter of expressing the shaded areas with the unshaded one.So yes we use (A-C)-(B-C) and then we get lucky and get A-B=50-20