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We are given a shape composed of a triangle and a trapezium. The area of the triangle is already known to be \( 28 \, \text{cm}^2 \). Our task is to find the area of the trapezium.

### Step-by-step approach:

1. **Dimensions:**
   - The total height of the figure (triangle + trapezium) is \( 7 \, \text{cm} \).
   - The height of the trapezium alone is \( 2 \, \text{cm} \) (as labeled).
   - The base of the trapezium is \( 5 \, \text{cm} \).

2. **Identify the height of the triangle:**
   The height of the triangle is \( 7 - 2 = 5 \, \text{cm} \).

3. **Calculate the missing side (top base of the trapezium):**
   We can use the area of the triangle formula:
   \[
   \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
   \]
   Given that the area of the triangle is \( 28 \, \text{cm}^2 \) and the height is \( 5 \, \text{cm} \), we can solve for the base:
   \[
   28 = \frac{1}{2} \times \text{base} \times 5
   \]
   \[
   \text{base} = \frac{28 \times 2}{5} = 11.2 \, \text{cm}
   \]
   So, the top base of the trapezium is \( 11.2 \, \text{cm} \).

4. **Calculate the area of the trapezium:**
   The formula for the area of a trapezium is:
   \[
   \text{Area of trapezium} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}
   \]
   where:
   - \( \text{base}_1 = 11.2 \, \text{cm} \) (top base),
   - \( \text{base}_2 = 5 \, \text{cm} \) (bottom base),
   - \( \text{height} = 2 \, \text{cm} \).

   Substituting the values:
   \[
   \text{Area of trapezium} = \frac{1}{2} \times (11.2 + 5) \times 2
   \]
   \[
   = \frac{1}{2} \times 16.2 \times 2
   \]
   \[
   = 16.2 \, \text{cm}^2
   \]

Thus, the area of the trapezium is \( 16.2 \, \text{cm}^2 \).

Let me know if you'd like further details or clarifications! Here are 5 related questions to deepen your understanding:

1. How would the area of the trapezium change if the height of the trapezium were doubled?
2. Can you find the perimeter of the combined shape (triangle + trapezium)?
3. What is the difference in the areas between the triangle and the trapezium?
4. If the top base of the trapezium was instead \( 12 \, \text{cm} \), what would the new area be?
5. Can you derive the formula for the area of a trapezium from basic geometric principles?

### Tip:
When solving for unknown dimensions, always check the formula you're using to ensure you're substituting the correct values—this helps avoid simple errors in calculations.

The shape below is made of a triangle and a trapezium. The area of the triangle is 28 cm². Work out the area of the trapezium.

Solve the problem of finding the area of a trapezium when given a combined shape of a triangle and trapezium. The area of the triangle is known to be 28 cm². This problem involves geometry concepts, such as calculating the area of triangles and trapeziums. Suitable for Grades 7-9 students.

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