Answer:
Area of ΔDEF = 6 [tex]in^{2}[/tex]
Step-by-step explanation:
In the given figure , one triangle has side = 2 inches and the other triangle has the corresponding side = 4 inches.
Triangles BAC and EDF are similar that is,
ΔBAC≈ΔEDF
Area of triangle = [tex] 0.5\times base\times height[/tex]
All the sides of the second triangle is enlargened by a factor of 2.
Since in the area equation , there is multiplication of two sides, hence the area factor = 4.
Area of ΔBAC = 4 [tex]\times[/tex] ΔDEF
24 [tex]in^{2}[/tex] = 4 [tex]\times[/tex] ΔDEF
Area of ΔDEF = [tex]\frac{24}{4}[/tex]
Area of ΔDEF = 6 [tex]in^{2}[/tex]
