https://file.aiquickdraw.com/mathbot/file/17277274394120cg5dhr7.jpg

Let's analyze the problem to calculate the value of \( x \).

### Information provided:
- The shape consists of four congruent parallelograms.
- The total shaded area is \( 192 \, \text{cm}^2 \).
- The overall width of the shape is \( 24 \, \text{cm} \).
- The height of the parallelogram is \( 5 \, \text{cm} \).
- We are asked to find the value of \( x \) (the base of each parallelogram).

### Step-by-Step Process:

1. **Area of one parallelogram**: 
   The area of a parallelogram is given by the formula:
   \[
   \text{Area} = \text{Base} \times \text{Height}
   \]
   The base is \( x \, \text{cm} \) and the height is \( 5 \, \text{cm} \), so the area of one parallelogram is:
   \[
   \text{Area of one parallelogram} = x \times 5 = 5x \, \text{cm}^2
   \]

2. **Total area of four parallelograms**: 
   Since there are 4 parallelograms, the total area is:
   \[
   \text{Total Area} = 4 \times (5x) = 20x \, \text{cm}^2
   \]

3. **Using the given total area**:
   The problem states that the total shaded area is \( 192 \, \text{cm}^2 \). So, we set up the equation:
   \[
   20x = 192
   \]
   
4. **Solving for \( x \)**:
   \[
   x = \frac{192}{20} = 9.6 \, \text{cm}
   \]

### Final Answer:
The value of \( x \) is \( 9.6 \, \text{cm} \).

Would you like more details or have any questions? 

### Related Questions:
1. What is the total perimeter of the combined shape?
2. How would the area change if each parallelogram had a height of 6 cm instead of 5 cm?
3. What is the area of a single parallelogram in this problem?
4. If only two parallelograms were joined, how would the total area compare?
5. Can the base of a parallelogram ever be negative, and why?

### Tip:
Always ensure that units of measurement are consistent throughout your calculations to avoid errors!

Four congruent parallelograms are joined to make the shape below. The total shaded area is 192 cm². Work out the value of x.

Learn how to find the value of x when four congruent parallelograms are joined to form a shape with a total shaded area of 192 cm². This problem covers key concepts in geometry and algebra, suitable for students in Grades 6-8.

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