Understanding Area and Scale Factors

This video tutorial covers seventh-grade lesson 15, module four, focusing on solving area problems using scale drawings. The lesson involves peer activities and provides a comprehensive understanding of calculating areas and scale factors for squares, circles, and rectangles. The tutorial includes examples and concludes with a summary of key concepts.

What is the primary focus of the lesson on solving area problems using scale drawings?

• Identifying side lengths

• Determining the volume

• Understanding scale factors and area

• Calculating the perimeter

If the side length of a square is tripled, what happens to its area?

• The area remains the same

• The area is tripled

• The area is doubled

• The area is increased nine times

How do you calculate the area of a circle?

• Pi times radius squared

• Base times height

• Length times width

• Side squared

What is the scale factor if a circle's radius is doubled?

• 2

• 8

• 4

• 1

When the length of a rectangle is halved, what happens to its area?

• The area is halved

• The area remains the same

• The area is quartered

• The area is doubled

What is the relationship between scale factors and area quotients?

• Area quotients are always smaller

• Scale factors multiplied together equal the area quotient

• There is no relationship

• Scale factors are always larger

If a square's side length is reduced to one-fifth, what is the percentage of the new area compared to the original?

• 4%

• 50%

• 20%

• 25%

In example two, what is the scale factor when the radius of a circle is reduced from four units to two units?

• 1/4

• 2

• 1/2

• 1

What percentage of the larger circle is not occupied by the smaller circle in example two?

• 100%

• 75%

• 50%

• 25%

In the final example, what is the area of the shaded region of the smaller drawing if the larger figure's shaded region is approximately 21.5 square inches?

• 10.5 square inches

• 15 square inches

• 5.4 square inches

• 7.74 square inches