Scale Factors and Area Ratios

The video tutorial explains how to compute actual areas from scale drawings. It covers four examples, demonstrating how to find the scale factor and use it to calculate areas. The tutorial highlights that the ratio of areas is the square of the scale factor, considering two dimensions. It concludes with a practical example involving a basketball court, reinforcing the concept of scale factor squared.

What is the relationship between the scale factor and the actual measurement?

• The scale factor is the actual measurement divided by the scale drawing.

• The scale factor is the scale drawing divided by the actual measurement.

• The scale factor is the difference between the scale drawing and the actual measurement.

• The scale factor is the sum of the scale drawing and the actual measurement.

In Example 1, what is the ratio of the area of the scale drawing to the actual area?

• 4 to 1

• 1 to 4

• 2 to 1

• 1 to 2

What happens to the area when the scale factor is less than 1, as shown in Example 2?

• The area of the scale drawing is twice the actual area.

• The area of the scale drawing is equal to the actual area.

• The area of the scale drawing is smaller than the actual area.

• The area of the scale drawing is larger than the actual area.

In Example 2, what is the scale factor used?

• 1/2

• 1/3

• 2/3

• 3/4

How is the area of a triangle calculated in Example 3?

• Base times height divided by 2

• Base times height

• Base minus height

• Base plus height

What is the scale factor for the triangles in Example 3?

• 3 to 2

• 2 to 3

• 4 to 3

• 3 to 4

What conclusion can be drawn about the scale factor and area ratio?

• The area ratio is the scale factor squared.

• The area ratio is the scale factor cubed.

• The area ratio is the scale factor halved.

• The area ratio is the scale factor doubled.

In the basketball court example, what is the actual area of the court?

• 500 feet squared

• 900 feet squared

• 600 feet squared

• 750 feet squared

How does the scale factor affect the dimensions of a drawing?

• It only affects the length.

• It only affects the width.

• It does not affect the dimensions.

• It affects both length and width.

What is the scale factor if 1 inch on the drawing represents 4 inches of actual length?

• 1/5

• 1/3

• 1/2

• 1/4