Question: Calculate the volume of the triangular prism shown below.
9 cm
3 cm
6 cm
8 cm
Not drawn accurately
center: Triangular prism; the front triangular face has base 9 cm and height 6 cm, with a side length labeled 8 cm and a vertical edge labeled 3 cm.
1. **State the problem:** We need to find the volume of a triangular prism with a triangular base having base $9$ cm and height $6$ cm, and the prism's length (height of the prism) is $3$ cm.
2. **Formula for volume of a triangular prism:**
$$\text{Volume} = \text{Area of triangular base} \times \text{length of prism}$$
3. **Calculate the area of the triangular base:**
The area of a triangle is given by:
$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
Substitute the values:
$$\text{Area} = \frac{1}{2} \times 9 \times 6 = \frac{1}{2} \times 54 = 27 \text{ cm}^2$$
4. **Calculate the volume:**
Multiply the area of the base by the length of the prism:
$$\text{Volume} = 27 \times 3 = 81 \text{ cm}^3$$
5. **Final answer:**
The volume of the triangular prism is $81$ cubic centimeters.