imc

The Pythagorean Inequality tells us that in an obtuse triangle, $a^2+b^2<c^2$. The triangle inequality tells us that $a+b>c$. So, we have two inequalities: $$x^2+y^2<1$$ $$x+y>1$$ The first equation is $\frac{1}{4}$ of a circle with radius $1$, and the second equation is a line from $(0,1)$ to $(1,0)$. So, the area is $\frac{\pi }{4}-\frac{1}{2}$ which is approximately $\boxed{\text{ 0.29}}$