1. **State the problem:** We need to find the volume of a prism with a hexagonal base. 2. **Given data:** - Area of the base $= 18$ cm$^2$ - Height of the prism $= 4$ cm - Other dimensions (5 cm and 7 cm) are given but not needed for volume calculation since volume depends on base area and height. 3. **Formula for volume of a prism:** $$\text{Volume} = \text{Base Area} \times \text{Height}$$ 4. **Apply the formula:** $$\text{Volume} = 18 \times 4$$ 5. **Calculate:** $$\text{Volume} = 72$$ 6. **Interpretation:** The volume of the prism is 72 cubic centimeters. **Final answer:** $$\boxed{72 \text{ cm}^3}$$