1. **State the problem:** We need to find the volume of a prism whose cross section is a parallelogram. The parallelogram has one pair of opposite sides 8 cm long and the distance (height) between these sides is 4 cm. The length (or height) of the prism is 1.2 cm.
2. **Formula for volume of a prism:**
The volume $V$ of a prism is given by:
$$V = \text{Area of cross section} \times \text{length of prism}$$
3. **Area of the parallelogram:**
The area $A$ of a parallelogram is:
$$A = \text{base} \times \text{height}$$
Here, base = 8 cm and height = 4 cm.
4. **Calculate the area:**
$$A = 8 \times 4 = 32 \text{ cm}^2$$
5. **Calculate the volume:**
Using the length of the prism $l = 1.2$ cm,
$$V = 32 \times 1.2 = 38.4 \text{ cm}^3$$
**Final answer:** The volume of the prism is $38.4$ cubic centimeters.
Prism Volume Af846E
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.