Dilations and Measurement

How do dilations affect the area and perimeter of a figure?

Tom's vegetable garden currently measures 10 ft by 10 ft. Tom w ants to change the size of his garden and will either use a scale factor of 2 or 1/2. Complete the following questions to observe how each scale factor would change the perimeter and the area of his garden.

Multiple Choice

What are the area and perimeter of the original garden?

• A = 20 ft²

  P = 40 ft

• A = 100 ft²

  P = 40 ft

• A = 100 ft²

  P = 20 ft

• A = 20 ft²

  P = 100 ft

Multiple Choice

What are the area and perimeter of the garden after being dilated by a scale factor of 2?

• A = 80 ft²

  P = 200 ft

• A = 40 ft²

  P = 80 ft

• A = 200 ft²

  P = 40 ft

• A = 400 ft²

  P = 80 ft

What do you notice?

What happened to the perimeter when Tom used a scale factor of 2?

What happened to the area?

Multiple Choice

What would be the area and perimeter of the new garden if it was dilated by a scale factor of 1/2?

• A = 100 ft²

  P = 20 ft

• A = 25 ft²

  P = 20 ft

• A = 20 ft²

  P = 25 ft

• A = 50 ft²

  P = 40 ft

What do you notice?

What happened to the perimeter when Tom used a scale factor of 1/2?

What happened to the area?

The need to know

When a figure is dilated by a scale factor of "x", its area changes by a factor of x^2.

Its perimeter changes by a factor of x.

Example

If a figure is dilated by a scale factor of 10, its area will change by a factor of 10² (100) and its perimeter will change by a factor of 10.

Original area: 49 ft² Original perimeter: 28 ft
New area:_____ ft² New perimeter:______ ft