This trapezoid-based right prism has a volume of
\[30\text{ cm}^3\].
A prism with bases that are trapezoids. The height of the prism is five centimeters. The trapezoid has a larger base of six centimeters. One slanted side of the trapezoid that connects from the larger base to the smaller base of the trapezoid is one centimeter.
\[6\text{ cm}\]
\[5\text{ cm}\]
\[1\text{ cm}\]
What is the area of the base of the prism?

To find the area of the base of the prism, we need to use the information provided and relate it to the volume of the prism. The prism's volume is given by the formula:

\[
V = A_{\text{base}} \times h
\]

where:
- \( V \) is the volume of the prism.
- \( A_{\text{base}} \) is the area of the base (the trapezoid in this case).
- \( h \) is the height of the prism.

From the problem:
- The volume \( V \) is \( 30 \text{ cm}^3 \).
- The height of the prism \( h \) is \( 5 \text{ cm} \).

Plugging these values into the volume formula, we get:

\[
30 = A_{\text{base}} \times 5
\]

Solving for \( A_{\text{base}} \):

\[
A_{\text{base}} = \frac{30}{5} = 6 \text{ cm}^2
\]

So, the area of the base of the prism is \( \mathbf{6 \text{ cm}^2} \).

Would you like to explore the geometry of the trapezoid further or have any other questions?

### Related Questions:
1. How do you calculate the volume of a right prism with different types of bases?
2. What is the formula for the area of a trapezoid?
3. How do you find the height of a trapezoid if given the area and bases?
4. What are the properties of a right prism?
5. How do you calculate the surface area of a trapezoidal prism?

### Tip:
When solving problems involving prisms, always identify the shape of the base and use the appropriate area formula for that shape.

Learn how to calculate the area of the base of a trapezoidal prism with a given volume of 30 cm³ and height of 5 cm. This problem involves applying the formula for the volume of a prism and solving for the base area. Suitable for students in Grades 7-9 studying geometry and prisms.

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