Triangle from Three Projections Area

A triangle in the $xy$-plane is such that when projected onto the $x$-axis, $y$-axis, and the line $y = x$, the results are line segments whose endpoints are $(1,0)$ and $(5,0)$, $(0,8)$ and $(0,13)$, and $(5,5)$ and $(7.5,7.5)$, respectively. What is the triangle's area?