Determine the missing side lengths in various geometric figures.

To solve the problem of determining the missing sides in the given figures, we will analyze each case step by step. Let's go through them one by one.

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1. Square (Figure 2)

- Given: Side of square \( B \) is 4 cm.
- Task: Determine the side of square \( A \).

Since both \( A \) and \( B \) are squares, their sides are equal to their respective dimensions.
- Side of square \( A \): \( 2 \) cm.

Answer: \( 2 \) cm.

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2. Rectangle (Figure 3)

- Given:
- Rectangle \( A \): Length = 4 cm, Width = 1.5 cm.
- Rectangle \( B \): Length = 8 cm, Width = ?.
- Task: Determine the width of rectangle \( B \).

The areas of rectangles \( A \) and \( B \) are proportional if they are similar. However, since no similarity is mentioned, we assume the problem is about matching areas or another specific condition. Without additional context, let's assume the problem is about matching areas.

Area of rectangle \( A \):
\[
\text{Area}_A = \text{Length} \times \text{Width} = 4 \times 1.5 = 6 \, \text{cm}^2
\]

Area of rectangle \( B \):
\[
\text{Area}_B = \text{Length} \times \text{Width} = 8 \times \text{Width}
\]

If the areas are equal:
\[
8 \times \text{Width} = 6
\]
\[
\text{Width} = \frac{6}{8} = 0.75 \, \text{cm}
\]

Answer: \( 0.75 \) cm.

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3. Irregular Shape (Figure 4)

- Given:
- Shape \( A \): Dimensions 10 cm and 15 cm.
- Shape \( B \): One side is 30 cm, and the other side is unknown (?).
- Task: Determine the missing side of shape \( B \).

This appears to be a scaling problem. If the shapes are similar, the ratio of corresponding sides should be the same.

Ratio of sides for \( A \):
\[
\text{Ratio} = \frac{15}{10} = 1.5
\]

Assuming the 30 cm side in \( B \) corresponds to the 10 cm side in \( A \):
\[
\text{Missing side in } B = 30 \times 1.5 = 45 \, \text{cm}
\]

Answer: \( 45 \) cm.

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4. Cross Shapes (Figure 5)

- Given:
- Cross \( A \): Arm length = 2 cm.
- Cross \( B \): Arm length = 6 cm.
- Task: Determine the missing side of cross \( A \).

The problem seems to be about the central square of the cross. If the crosses are similar, the central square's side length in \( A \) can be determined by the ratio of the arm lengths.

Ratio of arm lengths:
\[
\text{Ratio} = \frac{6}{2} = 3
\]

If the central square's side in \( B \) is not given, we assume the problem is about the arm lengths only. The missing side of cross \( A \) is already given as 2 cm.

Answer: \( 2 \) cm.

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5. Triangle (Figure 6)

- Given:
- Triangle \( A \): Sides 8 cm and 12 cm.
- Triangle \( B \): Sides 32 cm, 48 cm, and one side is unknown (?).
- Task: Determine the missing side of triangle \( B \).

If the triangles are similar, the ratio of corresponding sides should be the same.

Ratio of sides:
\[
\text{Ratio} = \frac{32}{8} = 4
\]

The missing side in \( B \) corresponds to the 12 cm side in \( A \):
\[
\text{Missing side in } B = 12 \times 4 = 48 \, \text{cm}
\]

However, 48 cm is already given as the base. This suggests the problem might be about the height or another side. Assuming it's about the third side, we use the Pythagorean theorem or trigonometry, but without more information, we assume the problem is about the scaling.

Answer: \( 48 \) cm (if assuming the base).

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6. Triangle (Figure 7)

- Given:
- Triangle \( A \): Sides 7 cm and 21 cm.
- Triangle \( B \): Sides 18 cm and one side is unknown (?).
- Task: Determine the missing side of triangle \( B \).

If the triangles are similar, the ratio of corresponding sides should be the same.

Ratio of sides:
\[
\text{Ratio} = \frac{21}{7} = 3
\]

The missing side in \( B \) corresponds to the 7 cm side in \( A \):
\[
\text{Missing side in } B = 7 \times 3 = 21 \, \text{cm}
\]

However, 21 cm is already given. This suggests the problem might be about the third side. Assuming it's about the third side, we use the Pythagorean theorem or trigonometry, but without more information, we assume the problem is about the scaling.

Answer: \( 6 \) cm (if assuming the third side).

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7. Triangle (Figure 8)

- Given:
- Triangle \( A \): Sides 5 cm, 8 cm, and 2.5 cm.
- Triangle \( B \): Sides 20 cm and one side is unknown (?).
- Task: Determine the missing side of triangle \( B \).

If the triangles are similar, the ratio of corresponding sides should be the same.

Ratio of sides:
\[
\text{Ratio} = \frac{20}{5} = 4
\]

The missing side in \( B \) corresponds to the 8 cm side in \( A \):
\[
\text{Missing side in } B = 8 \times 4 = 32 \, \text{cm}
\]

Answer: \( 32 \) cm.

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8. Triangle (Figure 9)

- Given:
- Triangle \( A \): Height = 14 cm.
- Triangle \( B \): Height = 4 cm, base = 5 cm.
- Task: Determine the missing side of triangle \( A \).

If the triangles are similar, the ratio of corresponding heights should be the same as the ratio of corresponding bases.

Ratio of heights:
\[
\text{Ratio} = \frac{14}{4} = 3.5
\]

The base of triangle \( A \) corresponds to the 5 cm base in \( B \):
\[
\text{Base in } A = 5 \times 3.5 = 17.5 \, \text{cm}
\]

Answer: \( 17.5 \) cm.

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Final Answers

1. \( 2 \) cm
2. \( 0.75 \) cm
3. \( 45 \) cm
4. \( 2 \) cm
5. \( 48 \) cm
6. \( 6 \) cm
7. \( 32 \) cm
8. \( 17.5 \) cm

\[
\boxed{2, 0.75, 45, 2, 48, 6, 32, 17.5}
\]