Equidissections of darts

We define the dart $D(a)$ to be the nonconvex quadrilateral whose vertices are $(0,1),(1,1),(1,0),(a,a)$ (in counterclockwise order), with $a>1$. Such a dart can be dissected into any even number of equal-area triangles. Here we investigate darts that can be dissected into an odd number of equal-area triangle.