Understanding Scale Factors and Area

The video tutorial explains how scaling a polygon affects its area, using examples with rectangles. It demonstrates that when a polygon's dimensions are scaled by a factor, the area changes by the square of that factor. The tutorial provides two examples: one where a rectangle is scaled down by a factor of one-half, resulting in an area one-fourth of the original, and another where a rectangle's area grows by a factor of nine, indicating a scale factor of three. The key takeaway is understanding the relationship between scale factors and area changes.

What is the relationship between the scale factor and the area of a polygon?

• The area is directly proportional to the scale factor.

• The area is inversely proportional to the scale factor.

• The area changes by the square of the scale factor.

• The area remains unchanged regardless of the scale factor.

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If a rectangle is scaled by a factor of one-half, what happens to its area?

• The area remains the same.

• The area becomes one-fourth.

• The area is halved.

• The area doubles.

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When scaling a polygon by a factor of 1/3, what fraction of the original area does the new area represent?

• 1/3

• 1/6

• 1/9

• 1/12

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In the new example, what was the original area of rectangle n?

• 15 square units

• 5 square units

• 10 square units

• 20 square units

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What was the area of rectangle p after scaling from rectangle n?

• 45 square units

• 35 square units

• 25 square units

• 55 square units

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What scale factor was used to go from rectangle n to rectangle p?

• 3

• 5

• 4

• 2

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How does the area change when the scale factor is 2?

• The area doubles.

• The area remains the same.

• The area triples.

• The area quadruples.

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What is the height of rectangle p in the new example?

• 9

• 7

• 5

• 3

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What is the width of rectangle p in the new example?

• 5

• 9

• 7

• 11

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How do you verify the scale factor by scaling down?

• By recalculating the area to match the original.

• By ignoring the dimensions.

• By halving the dimensions.

• By doubling the dimensions.

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