Question 621234
<pre>
It's too hard to count them when all the diagonals are drawn in there.

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D)



 )}}}{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),-cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180))



),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(.25,.5,F),
locate(-.35,.5,G),locate(-.52,-.05,H),locate(-.05,-.42,I),
locate(.45,-.05,J),




line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

So we'll just draw each diagonal only until it just touches the next
diagonal or corner and does not cross another diagonal. We draw diagonal 
BE:

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180))),
line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D)


 )}}}

That introduces 1 triangle ABE.  We draw in diagonal BD:

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180))





),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D),
line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

That adds two triangles, BDE and BCD so we have 3 triangles so far. 
We draw just enough of it until it touches the first diagonal at G:


{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),-.2245139883,.3090169944)





),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(-.35,.5,G),


line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

That adds 2 more triangles, ABG and AGE, so we now have 5 triangles so far.
Now we'll extend that diagonal until it touches the next diagonal at H:

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),-.363271264,-.1180339887)





),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(-.35,.5,G),locate(-.52,-.05,H),

line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

That adds 2 more triangles, ABH and BGH so there are now 7 triangles.  Now we  complete drawing the diagonal AC:

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),-cos(54*pi/180),-sin(54*pi/180))





),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(-.35,.5,G),locate(-.52,-.05,H),
line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

That adds 4 more triangles, ABC, GBC, HBC, and HCD, so now we have 11 triangles. Now we begin the diagonal AD, drawn until it touches the 
other diagonal at F:

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),.2245139883,.3090169944),

line(-cos(90*pi/180),sin(90*pi/180),-cos(54*pi/180),-sin(54*pi/180))





),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),locate(.25,.5,F),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(-.35,.5,G),locate(-.52,-.05,H),
line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

That adds 3 more triangles ABF, AGF, and AFE.  So now we have 14 triangles. Next we complete diagonal AD:

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),-cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),cos(54*pi/180),-sin(54*pi/180))





),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),locate(.25,.5,F),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(-.35,.5,G),locate(-.52,-.05,H),

line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

That adds 5 triangles, ABD, AHD, AED, FRD, and FED, so now we have
19 triangle. Now we start the last diagonal EC drawing just to the point 
where it touches the diagonal at J:

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),-cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(cos(18*pi/180),sin(18*pi/180),.363271264,-.11803339888)





),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),locate(.25,.5,F),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(-.35,.5,G),locate(-.52,-.05,H),
locate(.45,-.05,J),
line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

That adds 3 triangles, AEJ, FEJ, and EJD.  Now we have 22 triangles.
Now we extend the partial diagonal to where it just touches BD at I:

{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),-cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(cos(18*pi/180),sin(18*pi/180),0,-.3819660113)



),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(.25,.5,F),
locate(-.35,.5,G),locate(-.52,-.05,H),locate(-.05,-.42,I),
locate(.45,-.05,J),




line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}
 
That adds 3 triangles BEI, EIJ, and JID.  So now we have 25 triangles.
Finally we complete the last diagonal.





{{{drawing(200,200,-1.2,1.2,-1.2,1.2,
green(line(-cos(18*pi/180),sin(18*pi/180),cos(18*pi/180),sin(18*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),-cos(54*pi/180),-sin(54*pi/180)),

line(-cos(90*pi/180),sin(90*pi/180),cos(54*pi/180),-sin(54*pi/180)),

line(cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180))



),
locate(-1.1,.4,B),locate(1,.4,E),locate(-.05,1.2,A),
locate(-.65,-.83,C),locate(.6,-.83,D),locate(.25,.5,F),
locate(-.35,.5,G),locate(-.52,-.05,H),locate(-.05,-.42,I),
locate(.45,-.05,J),




line(cos(18*pi/180),sin(18*pi/180),0,1),
line(-cos(18*pi/180),sin(18*pi/180),0,1),
line(cos(18*pi/180),sin(18*pi/180),cos(54*pi/180),-sin(54*pi/180)),
line(-cos(18*pi/180),sin(18*pi/180),-cos(54*pi/180),-sin(54*pi/180)),
line(-cos(54*pi/180),-sin(54*pi/180),cos(54*pi/180),-sin(54*pi/180)) )}}}

That adds 6 triangles, BEC, BIC, HIC, DIC, JCD, and ECD.  So we 
end up with a grand total of 31 triangles. I don't think I've
missed any, or counted any twice.

Edwin</pre>