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To find the volume of the prism in the given image, we need to identify the shape of the base and the height of the prism. The base of this prism is a trapezoid, and the height of the prism is given as 5 inches.

The formula for the volume \( V \) of a prism is:

\[ V = B \times h \]

where \( B \) is the area of the base and \( h \) is the height of the prism.

First, let's find the area of the trapezoidal base. The formula for the area \( A \) of a trapezoid is:

\[ A = \frac{1}{2} \times (a + b) \times h_b \]

where \( a \) and \( b \) are the lengths of the parallel sides of the trapezoid, and \( h_b \) is the height of the trapezoid.

In this image:
- \( a = 4.7 \) inches (top base of the trapezoid)
- \( b = 4.7 \) inches (bottom base of the trapezoid)
- \( h_b = 5.2 \) inches (height of the trapezoid)

So, the area of the trapezoid is:

\[ A = \frac{1}{2} \times (4.7 + 4.7) \times 5.2 \]
\[ A = \frac{1}{2} \times 9.4 \times 5.2 \]
\[ A = \frac{1}{2} \times 48.88 \]
\[ A = 24.44 \text{ square inches} \]

Now, we can find the volume of the prism:

\[ V = 24.44 \times 5 \]
\[ V = 122.2 \text{ cubic inches} \]

So, the volume of the prism is \( 122.2 \) cubic inches.

Would you like further details or have any questions?

Here are five numbered questions you might ask:

1. How do you calculate the surface area of this prism?
2. What is the formula for the volume of a cylinder?
3. How do you find the volume of a cone?
4. Can you explain how to calculate the area of a parallelogram?
5. What is the volume formula for a sphere?

**Tip:** When solving for the volume of prisms, always ensure you correctly identify the shape of the base and use the corresponding area formula.

Learn how to calculate the volume of a prism with a trapezoidal base using the area formula of a trapezoid and the volume formula of a prism. Detailed step-by-step solution included.

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