Question

Compare and contrast the effects that a proportional dimension change has on perimeter and area of figures

Answer 1

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.

Answer 2

A proportional dimension will change the perimeter by the factor of itself. And will change the area by the factor of the dilation squared.