Folding Rectangle!

By looking at the graph, we see that $x+y=10 \implies y=10-x$ and we know by Pythagoras we have:

$x^{2}+5^{2}= y^{2}= (10-x)^{2}$ ;

$x^{2}+25=100-20x+x^{2}$ ;

$\implies 20x=75 \implies x=\frac{75}{20}= 3.75 \implies y=6.25$ ;

The area of the two white triangles= $2 \times \frac{1}{2} \times (3.75)\times (5)= 18.75$ ;

The area of the unfolded rectangle= $5\times 10= 50$ ;

The area of shaded region: $\frac{50-18.75}{2}=15.625$ .

Remark: the two white triangles have sides $5,x,$ and hypotenuse $y$ .