A triangle with area 5 cm² is dilated with a scale factor of 3. What is the area of the image, in square centimeters?

To find the area of a dilated triangle, we use the formula for the area after dilation. When a figure is dilated by a scale factor ( k ), the area is multiplied by ( k^2 ).

1. The original area of the triangle is 5 cm².
2. The scale factor ( k ) is 3.

Now we calculate the new area:

[

text{New Area} = text{Original Area} times k^2 = 5 , text{cm}^2 times (3^2)

]

[

text{New Area} = 5 , text{cm}^2 times 9 = 45 , text{cm}^2

]

Therefore, the area of the image after dilation is 45 cm².