Answer:
Area of ΔDEF is [tex]45\ cm^2[/tex].
Step-by-step explanation:
Given;
ΔABC and ΔDEF is similar and ∠B ≅ ∠E.
Length of AB = [tex]2\ cm[/tex] and
Length of DE = [tex]6\ cm[/tex]
Area of ΔABC = [tex]5\ cm^2[/tex]
Solution,
Since, ΔABC and ΔDEF is similar and ∠B ≅ ∠E.
Therefore,
[tex]\frac{Area\ of\ triangle\ 1}{Area\ of\ triangle\ 2} =\frac{AB^2}{DE^2}[/tex]
Where triangle 1 and triangle 2 is ΔABC and ΔDEF respectively.
If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
[tex]\frac{5}{Area\ of\ triangle\ 2} =\frac{2^2}{6^2}\\ \frac{5}{Area\ of\ triangle\ 2}=\frac{4}{36}\\ Area\ of\ triangle\ 2=\frac{5\times36}{4} =5\times9=45\ cm^2[/tex]
Thus the area of ΔDEF is [tex]45\ cm^2[/tex].
