Answer:
2.7 square inch
Step-by-step explanation:
[tex] \triangle BAC \sim \triangle EDF... (Given) \\[/tex]
[tex] \therefore [/tex] By area of similar triangle theorem:
[tex] \frac{A(\triangle BAC)}{A(\triangle EDF)} = \frac{BC^2}{EF^2} \\\\
\therefore \frac{6}{A(\triangle EDF)} = \frac{3^2}{2^2} \\\\
\therefore \frac{6}{A(\triangle EDF)} = \frac{9}{4} \\\\
\therefore A(\triangle EDF) = \frac{4\times 6}{9} \\\\
\therefore A(\triangle EDF) = \frac{24}{9} \\\\
\therefore A(\triangle EDF) = 2.6667\\\\
\huge \purple {\boxed {\therefore A(\triangle EDF) = 2.7\: in^2}} [/tex]
