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In this question, we are asked to calculate the perimeter of a trapezium (ABCD) after an enlargement with three different scale factors (2, 1.5, and 0.5). The given trapezium has the following side lengths:

- \( AB = 7 \, \text{cm} \)
- \( BC = 5 \, \text{cm} \)
- \( CD = 10 \, \text{cm} \)
- \( DA = 4 \, \text{cm} \)

### Step 1: Find the original perimeter
The perimeter of a trapezium is the sum of all its side lengths. So,

\[
\text{Perimeter of ABCD} = AB + BC + CD + DA
\]

Substituting the values:

\[
\text{Perimeter of ABCD} = 7 \, \text{cm} + 5 \, \text{cm} + 10 \, \text{cm} + 4 \, \text{cm} = 26 \, \text{cm}
\]

### Step 2: Calculate the perimeter after enlargements

- **Scale factor of 2**: Multiply the original perimeter by 2.

\[
\text{New perimeter} = 26 \, \text{cm} \times 2 = 52 \, \text{cm}
\]

- **Scale factor of 1.5**: Multiply the original perimeter by 1.5.

\[
\text{New perimeter} = 26 \, \text{cm} \times 1.5 = 39 \, \text{cm}
\]

- **Scale factor of 0.5**: Multiply the original perimeter by 0.5.

\[
\text{New perimeter} = 26 \, \text{cm} \times 0.5 = 13 \, \text{cm}
\]

### Final answers:
- Perimeter for scale factor of 2: **52 cm**
- Perimeter for scale factor of 1.5: **39 cm**
- Perimeter for scale factor of 0.5: **13 cm**

Would you like more details on these calculations, or have any other questions?

Here are some related questions you might find helpful:
1. How do we calculate the area of a trapezium before and after enlargement?
2. What happens to angles of a shape during enlargement?
3. How does changing the scale factor affect the area of a shape?
4. Can a scale factor be negative? If so, what does it mean?
5. What is the difference between enlargement and translation in transformations?

**Tip:** When enlarging a shape, the perimeter is directly proportional to the scale factor, but the area scales by the square of the factor!

Calculate the perimeter of a trapezium after an enlargement with given scale factors.

Learn how to calculate the perimeter of a trapezium with a given set of dimensions after enlargements with scale factors of 2, 1.5, and 0.5. This problem involves geometry, perimeter calculations, and understanding scale factors, suitable for students in Grades 9-10.

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