Question

a triangle with an area of 25 ft^2 is dilated by a factor of 3.5. the area of the dilated triangle is ___ square feet.(no pictures are included in the question.)

Answer 1

After dilation, the area of the resulting shape is equal to the product between the area of the original shape and the square of the scale factor:

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

The area of the original shape is 25 ft² and the scale factor is k=3.5, so the area of the shape after the dilation can be determined as:

$\begin{gathered} A_{\text{dilation}}=(3.5^2)\cdot25 \\ A_{\text{dilation}}=12.25\cdot25 \\ A_{\text{dilation}}=306.25ft^2 \end{gathered}$

After the dilation, the area will be 306.25 ft²