In the dark part 2

The 4 congruent blue triangles are the only points that should be shaded. Thanks to @Henry U for pointing out the triangles such as the yellow one should not be shaded.

Now, let's take a closer look:

If we coordinatize as shown, the lines that form one triangle are bounded by the lines $x=0$ , $y=x/4$ , and $y=3-4x$ and the vertices are shown.

The area of one triangle is then $\frac{1}{2} \cdot 3 \cdot \frac{12}{17} = \frac{18}{17}$ . The total area is $4 \cdot \frac{18}{17} = \frac {72}{17}$ and the answer is $72+17 = \boxed{89}$

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Note: I accidentally mislabelled the point (0,3) as (3,0). It does not affect the result.

We are left with $4$ triangles which we need to find the size of. We can do this by looking at similar triangles:

By comparing to the larger triangle, we can see that it has an edge ratio of $1:4$ , and a hypotenuse of length $3$ . By using Pythag, we can get the length of the smaller side $l$ : $\begin{aligned}l^2+(4l)^2&=3^2\\ l^2+16l^2&=9\\ 17l^2&=9\\ l\:&=\sqrt{\frac{9}{17}}\end{aligned}$ And now we can find the area: $\begin{aligned}A&=\frac{l\times4l}{2}=2l^2\\ A&=2\times\frac{9}{17}\\ A&=\frac{18}{17}\end{aligned}$ And as there are $4$ of these triangles, we can find the total area $4\times\frac{18}{17}=\frac{72}{17}$ giving us our final answer of $72+17=\boxed{89}$ .

Determine three lines in the positive quadrant: (1) line joining (0,1) and (1,-3), y=-4x+1,

(2) line joining (-1,0) and (3,1), y=(x+1)/4,

(3) line joining (0,1) and (3,1), y=1.

These three lines create one internal triangle surrounded by all three straight lines.

The three vertices of this triangle in the positive quadrant are determined by intersection of the above three lines as (0,1), (3,1) and (3/17,5/17). The area of this right triangle is = (18/17).

There is an identical triangle in all the four quadrants.

Total area =(4*18)/17 = 72/17,

Answer=72+17=89