When you dilate any shape by a scale factor k, the area of the resulting shape will be equal to the area of the original shape multiplied by the square of the factor:
[tex]A_{\text{dilation}}=k^2A_{\text{original}}[/tex]
If the original triangle has an area of 192cm² and it was dilated using scale factor k=1/2, then the area of the resulting triangle can be calculated as:
[tex]\begin{gathered} A_{\text{dilation}}=(\frac{1}{2})^2\cdot192 \\ A_{\text{dilation}}=\frac{1}{4}\cdot192 \\ A_{\text{dilation}}=48 \end{gathered}[/tex]
The area of the triangle after dilation by scale factor 1/2 is 48cm²
