I know that the area of a triangle is half the product of the base and the height, so I need to find those values. The base of the triangle is the segment along the line $y=6$ between the points where it intersects the lines $y=x$ and $y=-x$. To find those points, I can solve for $x$ when $y=6$ and $y=x$ or $y=-x$. For $y=x$, I get $6=x$, so the point is $(6,6)$. For $y=-x$, I get $6=-x$, so the point is $(-6,6)$. The base of the triangle is the distance between these two points, which is $12$ units. The height of the triangle is the distance from the base to the origin, which is also the intersection of the lines $y=x$ and $y=-x$. The origin is $(0,0)$, so the height is $6$ units. The area of the triangle is half the product of the base and the height, which is $\frac{1}{2}(12)(6)=36$ square units. 
What is the area of the triangle bounded by the lines $y=x,$ $y=-x,$ and $y=6$?