https://file.aiquickdraw.com/mathbot/file/1730172766051dch269bt.jpg

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

\[
\text{Volume} = \text{Area of trapezoidal base} \times \text{Height (depth of prism)}
\]

### Step 1: Find the Area of the Trapezoidal Base
The area \( A \) of a trapezoid can be calculated using the formula:
\[
A = \frac{1}{2} \times (a + b) \times h
\]
where:
- \( a \) and \( b \) are the lengths of the parallel sides (10 cm and 6 cm in this case),
- \( h \) is the height (5 cm).

Substitute the values:
\[
A = \frac{1}{2} \times (10 + 6) \times 5 = \frac{1}{2} \times 16 \times 5 = 40 \, \text{cm}^2
\]

### Step 2: Multiply by the Height (Depth) of the Prism
The depth of the prism is given as 15 cm. Therefore, the volume \( V \) is:
\[
V = 40 \times 15 = 600 \, \text{cm}^3
\]

### Final Answer
The volume of the trapezoidal prism is:
\[
\text{Volume} = 600 \, \text{cm}^3
\]

Would you like further explanation on this or have any questions?

---

1. What is the formula for the volume of a trapezoidal prism?
2. How do you calculate the area of a trapezoidal base?
3. What would the volume be if the depth changed?
4. How does changing the height of the trapezoid affect the volume?
5. What other methods exist for finding the volume of complex shapes?

**Tip:** Remember, for prisms, the volume formula is always the area of the base multiplied by the height (depth).

Find the volume of a trapezoidal prism with a base of 10 cm and 6 cm, a height of 5 cm, and a depth of 15 cm. This geometry problem guides you through the trapezoidal area formula and volume calculation, perfect for students in Grades 7-9.

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