Answer:
Area of ΔEDF = 4.5 in²
Step-by-step explanation:
In the figure attached,
ΔBAC ~ ΔEDF
Property of similarity,
" If two triangles are similar then their corresponding angles will measure the same."
Scale factor for ΔBAC to ΔEDF = [tex]\frac{\text{Side EF}}{\text{Side BC}}[/tex]
= [tex]\frac{3}{4}[/tex]
"Ratio of the area of similar triangles = Square of the ratio of their corresponding sides"
[tex]\frac{\text{Area of triangle FDE}}{\text{Area of triangle CAB}}[/tex] = [tex](\frac{3}{4})^2[/tex]
[tex]\frac{\text{Area of triangle FDE}}{8}=\frac{9}{16}[/tex]
Area of ΔEDF = [tex]\frac{9\times 8}{16}[/tex]
= 4.5 square inches
Therefore, area of ΔEDF = 4.5 in²
