Question

In this diagram, BAC~ EDF. if the area of BAC = 6 in, what is the area of EDF.

Answer 1

2.7 square inch

Explanation:

`\triangle BAC \sim \triangle EDF... (Given) \\`

`\therefore` By area of similar triangle theorem:

`(A(\triangle BAC))/(A(\triangle EDF)) = (BC^2)/(EF^2) \\\\</p><p>\therefore (6)/(A(\triangle EDF)) = (3^2)/(2^2) \\\\</p><p>\therefore (6)/(A(\triangle EDF)) = (9)/(4) \\\\</p><p>\therefore A(\triangle EDF) = (4* 6)/(9) \\\\</p><p>\therefore A(\triangle EDF) = (24)/(9) \\\\</p><p>\therefore A(\triangle EDF) = 2.6667\\\\</p><p>\huge \purple {\boxed {\therefore A(\triangle EDF) = 2.7\: in^2}}`