1. **State the problem:** Find the volume and surface area of the given composite triangular prism-like solid with base 4 cm, height 6 cm, and slanted side 4 cm. 2. **Volume formula for a prism:** $$\text{Volume} = \text{Base Area} \times \text{Length}$$ 3. **Surface area formula:** $$\text{Surface Area} = \text{Sum of all faces' areas}$$ 4. **Calculate the area of the triangular base:** The triangle has base $b=4$ cm and height $h=6$ cm. $$\text{Area} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 4 \times 6 = 12 \text{ cm}^2$$ 5. **Calculate the volume:** Assuming the prism length (depth) is equal to the slanted side $4$ cm, $$\text{Volume} = 12 \times 4 = 48 \text{ cm}^3$$ 6. **Calculate the surface area:** - Two triangular bases: $2 \times 12 = 24$ cm$^2$ - Three rectangular faces: - Base rectangle: $4 \times 4 = 16$ cm$^2$ - Height rectangle: $6 \times 4 = 24$ cm$^2$ - Slant rectangle: $4 \times 4 = 16$ cm$^2$ Sum of rectangles: $$16 + 24 + 16 = 56 \text{ cm}^2$$ Total surface area: $$24 + 56 = 80 \text{ cm}^2$$ **Final answers:** - Volume = $48$ cm$^3$ - Surface area = $80$ cm$^2$