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The problem provides a parallelogram with a height of 5 cm and one side length of 6 cm. The perimeter of the parallelogram is 30 cm, and the goal is to calculate the area.

### Steps to solve:

1. **Identify the missing side of the parallelogram:**
   - The formula for the perimeter \( P \) of a parallelogram is:
   \[
   P = 2(a + b)
   \]
   where \( a \) and \( b \) are the lengths of the sides.
   - We know the perimeter is 30 cm and one side is 6 cm. Let the other side be \( x \).
   \[
   30 = 2(6 + x)
   \]
   Solving for \( x \):
   \[
   15 = 6 + x \quad \Rightarrow \quad x = 9 \, \text{cm}
   \]
   So, the other side is 9 cm.

2. **Calculate the area of the parallelogram:**
   - The area \( A \) of a parallelogram is given by:
   \[
   A = \text{base} \times \text{height}
   \]
   - From the diagram, the base is 9 cm and the height is 5 cm:
   \[
   A = 9 \times 5 = 45 \, \text{cm}^2
   \]

Thus, the area of the parallelogram is **45 cm²**.

Would you like more details on the steps or have any other questions?

### Related Questions:
1. How do you find the height of a parallelogram if only the area and base are given?
2. What is the difference between the area of a rectangle and a parallelogram?
3. How would you calculate the area of a parallelogram if it were a slanted figure with angles given?
4. If the height was doubled, what would be the new area of the parallelogram?
5. How does the perimeter affect the shape of a parallelogram if only the sides are known?

**Tip:** The area of a parallelogram is always based on the perpendicular height, not the slant height.

Calculate the area of the parallelogram with a perimeter of 30 cm, one side of length 6 cm, and a height of 5 cm.

Learn how to calculate the area of a parallelogram with a perimeter of 30 cm, a base of 9 cm, and a height of 5 cm. This problem covers key geometric concepts, including the perimeter and area formulas for parallelograms. Suitable for students in Grades 6-8.

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