Answer with explanation:
1.In terms of Perimeter
For any 2 Dimensional shape, having fixed dimension, (Perimeter is calculated=S), and if the shape is dilated with Dilation factor k,that is the similar shape has the perimeter equal to Dilation factor multiplied by Perimeter of Pre -Image=k S).
If Dilation Factor <1,
Perimeter of image will be less than Pre image.
If , Dilation Factor >1
Perimeter of Image will be greater than Pre-Image.
Actual Perimeter of Shape = S
Dilation factor or Proportionality Constant = k
New Perimeter of Shape = k*S
2. In terms of Area
Let me explain this concept by taking a four sided Quadrilateral named square.
Suppose, Side of Square = a units
Area of Square = a²
If side is dilated by a factor of m units
Area of new Square obtained = (m a)²= m²a²
Area increases or decreases by m² units, if dilation factor<1,the area Decreases, and if Dilation Factor >1, area increases.
→So, when Shape is Dilated by a factor m ,or you can say constant of proportionality is m,then area of new Shape is (m²,)square of × area of original shape.