I know not maths to my eternal shame but
could you draw a square/rectangle around the pentagon where one line is on top of a line in the pentagon and the other three lines touch the remaining verts. Then calculate the area of the triangles formed around it. Then draw a line straight down from the vert opposite the line touching the square (parallel to the side of the square). Then draw a line from that same vert to form a triangle with an area equal to the difference in area between the two outer triangles on either side and cut along the diagonal line?
I don't expect this to be correct and I haven't showed full working but I'm hoping that this could at least be "helpful" to someone.
I realise I probably got the equation on the picture back to front, but there is probably a more correct way to express a calculation of the difference between two sums anyway?