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Math is very clever, and it solves the problem of the fourth grade intelligently.
Extend OE to point F of AB with de=af=3 and bf=4-3= 1.

of:ad=bf:ab= 1:4

of=5* 1/4=5/4

△abc=△abd=4*5/2= 10

△abo=5/4*4/2=5/2

△BOC =△ABC-△ABO =△Abd-△ABO = 10-5/2 = 7.5

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