Answer: Area of ΔABC is 2.25x the area of ΔDEF.
Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as
[tex]A=\frac{\sqrt{3} }{4} a^{2}[/tex]
with a as side of the triangle.
Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:
a₁ = 1.2a
Then, its area is
[tex]A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}[/tex]
[tex]A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}[/tex]
Triangle DEF is 20% smaller than the original, which means its side is:
a₂ = 0.8a
So, area is
[tex]A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}[/tex]
[tex]A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}[/tex]
Now, comparing areas:
[tex]\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )[/tex]
[tex]\frac{A_{1}}{A_{2}} =[/tex] 2.25
The area of ΔABC is 2.25x greater than the area of ΔDEF.
