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Dillesh4096
Find the area of the shaded region if ABCD is a square of side 4 units and E is the midpoint of side BC.

A. 2
B. 8/3
C. 4
D. 16/3
E. None of these

\(\triangle {CFE}\) and \(\triangle {DFA}\) are similar so when we draw an altitude passing through F, the height or altitude of both triangles will be in ratio 2/4 or 1/2.
Thus if smaller altitude is x, bigger altitude = 2x and \(x+2x=4..x=\frac{4}{3}\)
Area of ABED = \(\frac{4+2}{2}*4=12\)=area of shaded region \(+4+\frac{16}{3}\)..
area of shaded region =\(12-\frac{28}{3}=\frac{36-28}{3}=8/3\)

B


how are triangles CFE and DFA similar?
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