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What theorem/theorems should be used to find the shaded area?

Y and M lie on the sides Ab and Bc respectively of the triangle YMB such that AY/MI= 1/4 and O/M = 1/3.

Area ABC=35 PC and QA intersect at X

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Please do re-post the figure with letters on the vertices/intersection points of segments...and include the explicit info on the areas/sides given. –  DonAntonio Sep 21 '13 at 17:02
    
You need the ratio of the split on the right side (and the left, which seems to be given). After that, it's just using the proportion of areas. –  Calvin Lin Sep 21 '13 at 17:07
    
What you need is this: Let $T_1$ and $T_2$ be triangles with the same height. Then the ratio of their areas is the same as the ratio of their bases. –  André Nicolas Sep 21 '13 at 17:09
    
@DonAntonio I have added the details –  Berry Sep 21 '13 at 17:53
    
Sorry @Berry, I can't see how to do it. Either I'm missing something basic or some other data is missing (like similarity between some little triangles or the like...) –  DonAntonio Sep 21 '13 at 18:23
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