Understanding Scale Factors and Their Effects

The video tutorial explains how dilation affects the perimeter and area of geometric shapes, using a rectangle as an example. It demonstrates that when a shape is scaled by a factor, the perimeter scales by the same factor, while the area scales by the square of the factor. The tutorial concludes by applying these principles to solve problems involving scaled shapes.

What is the initial task mentioned in the video regarding Pentagon A and Pentagon B?

• To compare the colors of the pentagons.

• To draw Pentagon B from scratch.

• To find the missing measurements in a table.

• To calculate the volume of Pentagon A.

When a rectangle is scaled by a factor of three, what happens to its perimeter?

• It remains the same.

• It doubles.

• It triples.

• It quadruples.

If the original rectangle has a perimeter of 6, what is the perimeter after scaling by a factor of three?

• 30

• 12

• 18

• 24

How does the area of a rectangle change when scaled by a factor of three?

• It increases by a factor of nine.

• It triples.

• It doubles.

• It remains unchanged.

What is the new area of a rectangle if the original area is 2 square units and it is scaled by a factor of three?

• 6 square units

• 9 square units

• 12 square units

• 18 square units

If a shape's perimeter scales linearly with the scale factor, what happens to the perimeter when the scale factor is three?

• It becomes half.

• It becomes three times larger.

• It becomes nine times larger.

• It remains the same.

What mathematical operation is used to determine the new area when both dimensions of a shape are scaled by the same factor?

• Addition

• Division

• Multiplication

• Subtraction

If the new area of a shape is 72 square units after scaling, what was the original area if the scale factor was three?

• 32 square units

• 24 square units

• 16 square units

• 8 square units

What is the relationship between the scale factor and the scaling of area?

• Area scales with the cube of the scale factor.

• Area does not change with the scale factor.

• Area scales with the square of the scale factor.

• Area scales linearly with the scale factor.

In the context of scaling, what does the term '3 squared' refer to?

• 3 multiplied by 2

• 3 multiplied by 3

• 3 added to 3

• 3 divided by 3