∵AE:EC=1:2,BF:FA=1:3,CG:GB=1:4
∴AE=1/3AC,CE=2/3AC;BF=1/4AB,AF=3/4AB;CG=1/5BC,BG=4/5BC
S△AEF:S△ABC=1/3AC*3/4AB/(AC*AB)
∴S△AEF=1/4S△ABC
S△BFG:S△ABC=1/4AB*4/5BC/(AB*BC)
∴S△BFG=1/5S△ABC
S△CEG:S△ABC=2/3AC*1/5BC/(AC*BC)
∴S△CFG=2/15S△ABC
S△ABC-S△AEF-S△BFG-S△CFG=40
S△ABC-1/4S△ABC-1/5S△ABC-2/15S△ABC=40
S△ABC=96