I'm going to assume the 2 shapes are both squares. ABCD has side of 4, BPQR has side of 5.
BP=5 AB=4 We can use Pythagorean theorem to see easily that AR= sqrt(5^2-4^2)=3.
Next step, we can see that angle A and angle D are both equal to 90 degrees. And angle DRS = <A+<ABR-<BRQ (exterior angles theorem) and <BRQ - <A= 90 degrees. Therefore...
triangle DRS is similar to triangle ABR so RD/SD=AB/AR=4/3
and RD=5-3=2 So SD is 3/2 because 2/ 3/2= 2*2/3 = 4/3 like above.
Now we can find shaded area by subtraction from square ABCD.
16-3*4/2-2*(3/2) /2=16-6-3/2=10-3/2=17/2.
I hope this answer helped if you have any question just ask in the comment!