To calculate the volume of the given prism, we can use the following steps:

1. Identify the base shape:
   The base of the prism appears to be a trapezoid.

2. Area of the trapezoidal base:
   The formula for the area of a trapezoid is:
   $A = \frac{1}{2} \cdot (a + b) \cdot h$ where:

   • $a$ and $b$ are the lengths of the parallel sides,
   • $h$ is the height (perpendicular distance between the parallel sides).

   In this case:

   • $a = 4 \, \text{m}$ (shorter parallel side),
   • $b = 5 \, \text{m}$ (longer parallel side),
   • $h = 4 \, \text{m}$ (distance between the parallel sides).

   Substitute the values: $A = \frac{1}{2} \cdot (4 + 5) \cdot 4 = \frac{1}{2} \cdot 9 \cdot 4 = 18 \, \text{m}^2$

3. Volume of the prism:
   The volume of a prism is given by:
   $V = \text{Base Area} \cdot \text{Height of the prism}$ Here, the height of the prism is the length perpendicular to the base (7 m).

   Substitute the values: $V = 18 \cdot 7 = 126 \, \text{m}^3$

Final Answer:

The volume of the prism is 126 cubic meters (m³).

Let me know if you'd like further explanation or have additional questions!

5 Follow-up Questions:

1. What is the difference between a prism and a pyramid in terms of volume calculation?
2. How does the orientation of the prism affect its volume?
3. How would the volume change if one dimension of the trapezoid base doubled?
4. What real-world applications use trapezoidal prisms?
5. How can you verify the units in volume calculations?

Tip: Always double-check the units of your measurements to ensure they are consistent throughout the calculation!