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