Scale Factors and Area Ratios

Mrs. Zaia's lesson focuses on computing actual areas from scale drawings. Students learn to identify scale factors and calculate areas in both scale drawings and actual pictures. Through examples, the lesson demonstrates how the scale factor affects area calculations, concluding that the area ratio is the square of the scale factor. The lesson includes practical exercises, such as calculating the area of a basketball court, to reinforce these concepts.

What is the primary goal of the lesson on computing actual areas from scale drawings?

• To learn how to draw scale drawings accurately

• To identify scale factors and compute actual areas

• To calculate the perimeter of scale drawings

• To understand the history of scale drawings

In Example 1, if the actual length is 4 and the scale drawing length is 8, what is the scale factor?

• 8

• 4

• 2

• 1

What is the area of the scale drawing in Example 1 if the scale length is 8 and the width is 6?

• 24 square units

• 36 square units

• 60 square units

• 48 square units

In Example 2, what is the scale factor when the actual base is 6 units and the scale drawing base is 8 units?

• 1/2

• 4/3

• 3/4

• 2

What is the relationship between the scale factor and the area ratio as observed in Examples 1 through 3?

• The area ratio is the scale factor cubed

• The area ratio is the scale factor squared

• The area ratio is double the scale factor

• The area ratio is half the scale factor

In Example 4, if 1 inch on the scale drawing corresponds to 15 feet of actual length, what is the scale factor?

• 15

• 1/30

• 30

• 1/15

What is the actual area of the half-court basketball plan if the length is 30 feet and the width is 25 feet?

• 750 square feet

• 600 square feet

• 500 square feet

• 900 square feet

In the final example, what is the scale factor if the area of the drawing is 9 square units and the actual area is 36 square units?

• 1/2

• 1/3

• 1/4

• 1/6

How does the scale factor relate to the actual length in the final example?

• The scale factor is the square root of the actual length

• The scale factor is half the actual length

• The scale factor is the reciprocal of the actual length

• The scale factor is the square of the actual length

What is the key takeaway regarding the relationship between scale factors and area ratios?

• Area ratios are unrelated to scale factors

• Area ratios are the square of scale factors

• Area ratios are the cube of scale factors

• Area ratios are the inverse of scale factors