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.