$y=x+1$ and $y=-x+1$ have $y$-intercepts at $(0,1)$ and slopes of 1 and $-1$, respectively. Since the product of these slopes is $-1$, the two lines are perpendicular. From $y=5$, we see that $(-4,5)$ and $(4,5)$ are the other two intersection points, and they are 8 units apart. By symmetry, this triangle is a $45-45-90$ triangle, so the legs are $4 \sqrt{2}$ each and the area is $\frac{(4 \sqrt{2})^{2}}{2}=(\mathbf{E}) 16$. 
What is the area of the triangle formed by the lines $y=5, y=1+x$, and $y=1-x$? (2019 AMC 8 Problems, Question \#21) 
* $$4$$ 
* $$8$$ 
* $$10$$ 
* $$12$$ 
* $$16$$ 