To find the volume of the given solid, we need to analyze the shape and apply the appropriate volume formula. The diagram depicts a prism with a trapezoidal base.

Step 1: Determine the Area of the Trapezoidal Base

The formula to find the area $A$ of a trapezoid is: $A = \frac{1}{2} \times (a + b) \times h$ where:

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

From the diagram:

• $a = 4 \, \text{m}$
• $b = 5 \, \text{m}$
• $h = 2 \, \text{m}$

Substituting these values into the formula: $A = \frac{1}{2} \times (4 \, \text{m} + 5 \, \text{m}) \times 2 \, \text{m} = \frac{1}{2} \times 9 \, \text{m} \times 2 \, \text{m} = 9 \, \text{m}^2$

Step 2: Calculate the Volume of the Prism

The volume $V$ of a prism is given by: $V = \text{Base Area} \times \text{Height of the Prism}$ From the diagram:

• Height of the prism (length perpendicular to the base) = $2 \, \text{m}$

Substituting the values: $V = 9 \, \text{m}^2 \times 2 \, \text{m} = 18 \, \text{m}^3$

Final Answer

The volume of the solid is $18 \, \text{m}^3$.

Would you like to explore any details or have any questions? Here are some related problems you might find interesting:

1. What is the volume of a cylinder with a radius of 3 m and height of 5 m?
2. How do you find the volume of a pyramid with a rectangular base?
3. What is the surface area of the trapezoidal prism shown in the image?
4. How does the volume change if the height of the prism is doubled?
5. Can you derive the formula for the volume of a cone?

Tip: When dealing with composite shapes, try breaking them down into simpler components whose areas or volumes you can easily calculate.