https://file.aiquickdraw.com/mathbot/file/1730375076889944j0ft0.jpg

The shape shown in the image is a trapezoidal prism. To find the volume of a trapezoidal prism, we use the formula:

\[
\text{Volume} = \text{Base Area} \times \text{Height of the Prism}
\]

1. **Calculate the Area of the Trapezoidal Base**:
   The formula for 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 (5 mm and 9 mm).
   - \( h \) is the height of the trapezoid (3 mm).

   Plugging in the values:
   \[
   A = \frac{1}{2} \times (5 + 9) \times 3 = \frac{1}{2} \times 14 \times 3 = 21 \text{ mm}^2
   \]

2. **Calculate the Volume of the Prism**:
   Now, we multiply the area of the trapezoidal base by the height (or depth) of the prism, which is 4 mm.
   \[
   \text{Volume} = 21 \times 4 = 84 \text{ mm}^3
   \]

So, the volume of the trapezoidal prism is **84 cubic millimeters**.

Would you like further details or have any questions?

### Related Questions
1. How do we calculate the surface area of a trapezoidal prism?
2. What if the prism had a different height? How would the volume change?
3. How does the formula for the area of a trapezoid apply to other shapes?
4. What units would the volume be in if the dimensions were given in centimeters?
5. How can we calculate the volume if only the perimeter of the base and height of the prism are known?

### Tip
Always ensure that all measurements are in the same units before calculating volume.

Find the volume of a trapezoidal prism with a base area calculated using the trapezoid formula and prism height. This example involves dimensions of 5 mm, 9 mm, 3 mm, and 4 mm, covering concepts like volume and area of trapezoids, suitable for Grades 6-8.

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