Scale Factors and Area Ratios

The video tutorial explores area relationships through three examples, focusing on calculating scale factors and understanding their impact on area. Example 1 demonstrates finding the scale factor and area ratio. Example 2 further explores these concepts with different dimensions. Example 3 focuses on triangles, illustrating how scale factors affect area. The tutorial concludes with observations on the relationship between scale factors and area ratios.

What is the scale factor if the original length is 4 units and the scaled length is 8 units?

• 4

• 1

• 2

• 3

If the area of the original figure is 12 square units and the scaled figure is 48 square units, what is the ratio of the scaled area to the original area?

• 3

• 2

• 5

• 4

In Example 2, what is the scale factor when the original length is 6 units and the scaled length is 2 units?

• 1/3

• 1/4

• 1/2

• 1/5

What is the area of the scaled figure in Example 2 if the original area is 54 square units?

• 12

• 6

• 9

• 15

How does the scale factor relate to the area ratio in Example 2?

• The area ratio is half the scale factor

• The area ratio is the square of the scale factor

• The area ratio is unrelated to the scale factor

• The area ratio is double the scale factor

In Example 3, what is the scale factor if the original base is 9 units and the scaled base is 12 units?

• 4/3

• 6/3

• 3/4

• 5/3

What is the area of the scaled triangle in Example 3 if the original area is 27 square units?

• 36

• 54

• 48

• 42

Is the transformation in Example 3 an enlargement or a reduction?

• Enlargement

• Reduction

• Neither

• Both

What conclusion can be drawn about the relationship between scale factors and area ratios?

• Area ratio is the square of the scale factor

• Area ratio is the cube of the scale factor

• Area ratio is unrelated to the scale factor

• Area ratio is the same as the scale factor

When the scale factor of the sides was 4/3, what was the value of the area ratio?

• 9/16

• 16/9

• 4/3

• 3/4