This is another collection of puzzles from Catriona Agg.
Answer #1 (rev)___ Answer #2 ___ Answer #3 ___ Answer #4 ___ Answer #5 ___ Answer #6
See Geometric Puzzle Musings (rev) for solutions.
Meditations on Mathematics
A compendium of puzzles, problems, math inquiries, and math commentary.
My working for puzzle #1
Your answer is 5/8.
My answer is 1/2.
Let ABC be triangle, counterclockwise with A as top vertex. D is midpoint of AB. E and F are points on AC such that AE=EF=FC. Join DE, BE, BF.
trn ADE = trn DBE = 1 say
trn ADE + trn DBE = 1+1=2 = trn AEB
Also trn AEB = trn EFB = trn FCB = 2
Total area ABC = 2+2+2=6
Total shaded area DEFB = trn DBE + trn EFB = 1+2=3
Shaded area as fraction of total ABC = 3/6=1/2
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Your are correct. Thank you. Clearly I misread the figure.