Similar Polygons and Scale Factor Worksheet with eight problems requiring students to calculate scale factors between pairs of similar polygons.

To solve the problem of finding the scale factor from the smaller figure to the larger figure for each pair of similar polygons, we need to compare corresponding sides of the polygons. The scale factor is the ratio of the length of a side of the larger polygon to the length of the corresponding side of the smaller polygon.

Let's go through each problem step by step:

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Problem 1:

- Larger triangle: Sides are 35, 30, 15.
- Smaller triangle: Sides are 21, 18, 9.

Choose any pair of corresponding sides:
- Larger side: 35
- Smaller side: 21

Scale factor = \( \frac{\text{Larger side}}{\text{Smaller side}} = \frac{35}{21} = \frac{5}{3} \).

Answer for Problem 1: \( \frac{5}{3} \)

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Problem 2:

- Larger rectangle: Sides are 48, 30.
- Smaller rectangle: Sides are 40, 25.

Choose any pair of corresponding sides:
- Larger side: 48
- Smaller side: 40

Scale factor = \( \frac{\text{Larger side}}{\text{Smaller side}} = \frac{48}{40} = \frac{6}{5} \).

Answer for Problem 2: \( \frac{6}{5} \)

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Problem 3:

- Larger square: Side = 63.
- Smaller square: Side = 54.

Choose the sides:
- Larger side: 63
- Smaller side: 54

Scale factor = \( \frac{\text{Larger side}}{\text{Smaller side}} = \frac{63}{54} = \frac{7}{6} \).

Answer for Problem 3: \( \frac{7}{6} \)

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Problem 4:

- Larger square: Side = 432.
- Smaller square: Side = 414.

Choose the sides:
- Larger side: 432
- Smaller side: 414

Scale factor = \( \frac{\text{Larger side}}{\text{Smaller side}} = \frac{432}{414} = \frac{72}{69} = \frac{24}{23} \).

Answer for Problem 4: \( \frac{24}{23} \)

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Problem 5:

- Larger rectangle: Length = 45, Width = 40.
- Smaller rectangle: Length = 30, Width = 30.

Choose the lengths (or widths, as they are proportional):
- Larger length: 45
- Smaller length: 30

Scale factor = \( \frac{\text{Larger length}}{\text{Smaller length}} = \frac{45}{30} = \frac{3}{2} \).

Answer for Problem 5: \( \frac{3}{2} \)

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Problem 6:

- Larger right triangle: Sides are 16, 12, 20.
- Smaller right triangle: Sides are 8, 6, 10.

Choose any pair of corresponding sides:
- Larger side: 16
- Smaller side: 8

Scale factor = \( \frac{\text{Larger side}}{\text{Smaller side}} = \frac{16}{8} = 2 \).

Answer for Problem 6: \( 2 \)

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Problem 7:

- Larger rectangle: Length = 15, Width = 10.
- Smaller rectangle: Length = 6, Width = 4.

Choose the lengths (or widths, as they are proportional):
- Larger length: 15
- Smaller length: 6

Scale factor = \( \frac{\text{Larger length}}{\text{Smaller length}} = \frac{15}{6} = \frac{5}{2} \).

Answer for Problem 7: \( \frac{5}{2} \)

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Problem 8:

- Larger trapezoid: Bases are 12 and 6, Height = 9.
- Smaller trapezoid: Bases are 8 and 6, Height = 6.

Choose the longer bases:
- Larger base: 12
- Smaller base: 8

Scale factor = \( \frac{\text{Larger base}}{\text{Smaller base}} = \frac{12}{8} = \frac{3}{2} \).

Answer for Problem 8: \( \frac{3}{2} \)

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Final Answers:

\[
\boxed{\frac{5}{3}, \frac{6}{5}, \frac{7}{6}, \frac{24}{23}, \frac{3}{2}, 2, \frac{5}{2}, \frac{3}{2}}
\]