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.