The answer is 7/4. The process is as follows: triangle ADE is similar to triangle ABC, with similarity ratio 1:2 and area ratio 1:4, so the area of △ABC is 4S, and the areas of △ABE and △CBE are 2S respectively. In the proof of do: of = de: BF = 1: 3, it can be proved that O is the midpoint of DG, and it is easy to know that the △DEG area is half that of ADE, that is, 0.5S, so the △EOG area is1s.

So the BOGC area of the quadrilateral is equal to the delta △BEC area minus the delta △EOG area, which is equal to 7/4.

I hope I can help you. This is the second sub-question of the first question of 1 1 Neijiang, Sichuan.