Considering similar triangle ratios.
3 = (3+x)
y = (4+y)
Where x and y are the width and length of the inscribed rectangle ascribing the red region respectively.
Cross Multiply.
12+3y = 3y+xy
xy = 12 square units.
Therefore;
Area Red Region is;
½(xy)
= ½(12)
= 6 square units.
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