Answer:
Let A be the area of the dilated triangle.
Given the statement: A triangle with an area of 2/3 cm2 is dilated by a factor of 6.
⇒ Pre-image triangle has an area = [tex]\frac{2}{3}[/tex] [tex]cm^2[/tex]
Scale factor(k) states that the dimension of the Dilated-image is 6 times longer than the dimensions of the pre-image.
i.e,
[tex]k = \frac{\text{Dilation image}}{\text{Pre-image}}[/tex]
Substitute the given values to find the value of area of dilated triangle.
[tex]6 = \frac{A}{\frac{2}{3} }[/tex]
or
[tex]6 = \frac{3A}{2}[/tex]
Multiply both sides by 2 we get;
[tex]12 = 3A[/tex]
Divide both sides by 3 we get;
[tex]4 = A[/tex]
Therefore, the area of the dilated triangle is, [tex]4 cm^2[/tex]
