Question

If Heather's triangle is dilated by a scale factor of 1\2,what is the area of the new triangle?1) 48cm^22) 216cm^23) 144cm^24) 108cm^2

Answer 1

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:

`A_{\text{dilation}}=k^2A_{\text{original}}`

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:

`\begin{gathered} A_{\text{dilation}}=((1)/(2))^2\cdot192 \\ A_{\text{dilation}}=(1)/(4)\cdot192 \\ A_{\text{dilation}}=48 \end{gathered}`

The area of the triangle after dilation by scale factor 1/2 is 48cm²