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Step-by-step explanation:
Let the side of the triangle be 'a' units
Therefore by Pythagoras theorem in ∆ADC we have,
AD²+CD²=AC²
AC²= a²+a²
AC²=2a²
AC=a√2 units
Since ∆ACF ~∆BCE
ar(∆ACF)/ar(∆BCE)
=AC²/BC²
=(√2a)²/a²
=2a/a
=2
Or simply
1/2 ar(∆ACF)=ar(∆BCE)
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