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Let's break this problem down step by step.

### Given:
- The shapes are a **triangular pyramid** and a **triangular prism** with congruent bases and equal heights.

For both shapes:
- **Base area** = \( \frac{1}{2} \times \text{base} \times \text{height of base} \)
- **Base** = 14 m
- **Height of base** = 2 m
- The height of both the pyramid and the prism is 6 m.

### Step 1: Find the area of the base (common to both shapes):
\[
\text{Base Area} = \frac{1}{2} \times 14 \, \text{m} \times 2 \, \text{m} = 14 \, \text{m}^2
\]

### Step 2: Volume of the Pyramid
The volume \( V \) of a pyramid is given by:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Substitute the values:
\[
V = \frac{1}{3} \times 14 \, \text{m}^2 \times 6 \, \text{m} = \frac{1}{3} \times 84 = 28 \, \text{m}^3
\]

### Step 3: Volume of the Prism
The volume \( V \) of a prism is given by:
\[
V = \text{Base Area} \times \text{Height}
\]
Substitute the values:
\[
V = 14 \, \text{m}^2 \times 6 \, \text{m} = 84 \, \text{m}^3
\]

### Step 4: Relationship between the Volumes
The volume of the pyramid is:
\[
V_{\text{pyramid}} = \frac{1}{3} \times V_{\text{prism}}
\]

### Conclusion:
(a) Volume of the pyramid = \( 28 \, \text{m}^3 \)

(b) Volume of the prism = \( 84 \, \text{m}^3 \)

(c) Volume of the pyramid = \( \frac{1}{3} \times \) Volume of the prism.

The correct equation is: **This equation is true for all triangular prisms and triangular pyramids with congruent bases and equal heights.**

Would you like any additional details or clarifications?

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Here are 5 related questions you can explore:
1. How do you calculate the surface area of a triangular prism?
2. What is the formula for the volume of other types of pyramids, like square or rectangular pyramids?
3. How does the volume formula differ for cones and pyramids?
4. How would the answer change if the height of the pyramid were different from the prism?
5. How can we verify the congruency of the bases in different 3D shapes?

**Tip:** When comparing volumes of similar shapes, always check if they share the same base and height to simplify the calculations.

The triangular pyramid and triangular prism shown below have congruent bases and equal heights. Complete the following by calculating the volume of the pyramid, the volume of the prism, and their relationship.

Calculate the volume of a triangular pyramid and triangular prism with congruent bases and equal heights. This geometry problem involves using key formulas for volume calculation, providing a step-by-step solution suitable for Grades 8-10.

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