Question: Calculate the volume of the triangular prism shown below.
11 cm
5 cm
6 cm
9 cm
Graph/shape: a yellow triangular prism-like figure centered on the page; top horizontal edge labeled 11 cm, left vertical edge labeled 5 cm, inner vertical height labeled 6 cm, and lower left slanted edge labeled 9 cm. position_hint = center
1. **State the problem:** Calculate the volume of the given triangular prism with base edges and height labeled.
2. **Formula for volume of a triangular prism:**
$$V = \text{Base Area} \times \text{Length}$$
3. **Identify the base triangle dimensions:**
- The base triangle has sides 5 cm, 6 cm (height), and 9 cm (slanted side).
- The length of the prism (the prism's length along which the base is extruded) is 11 cm.
4. **Calculate the area of the triangular base:**
- The base area formula for a triangle is:
$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
- Here, base = 5 cm and height = 6 cm.
5. **Calculate the base area:**
$$\text{Area} = \frac{1}{2} \times 5 \times 6 = \frac{1}{2} \times 30 = 15 \text{ cm}^2$$
6. **Calculate the volume of the prism:**
$$V = \text{Base Area} \times \text{Length} = 15 \times 11 = 165 \text{ cm}^3$$
7. **Final answer:**
The volume of the triangular prism is $$165 \text{ cm}^3$$.