Answer:
Area of ΔEDF = 2.7 in²
Step-by-step explanation:
It's given in the question,
ΔBAC ~ ΔEDF
In these similar triangles,
Scale factor of the sides = [tex]\frac{\text{Measure of one side of triangle BAC}}{\text{Measure of one side of triangle EDF}}[/tex]
[tex]=\frac{\text{BC}}{\text{EF}}[/tex]
[tex]=\frac{3}{2}[/tex]
Area scale factor = (Scale factor of the sides)²
[tex]\frac{\text{Area of triangle BAC}}{\text{Area of triangle EDF}}=(\frac{3}{2})^2[/tex]
[tex]\frac{6}{\text{Area of triangle EDF}}=(\frac{9}{4})[/tex]
Area of ΔEDF = [tex]\frac{6\times 4}{9}[/tex]
= 2.67
≈ 2.7 in²
Therefore, area of the ΔEDF is 2.7 in²
