1. **Problem statement:** Calculate the surface area of a pyramid with given base and slant heights. 2. **Formula:** The surface area $A$ of a pyramid is given by $$A = B + \frac{1}{2} P l$$ where $B$ is the base area, $P$ is the perimeter of the base, and $l$ is the slant height. 3. **Step-by-step solution for the first pyramid:** - Given: base side length $4$ cm, slant height $6$ cm, base area $64$ cm$^2$ (likely a square base). - Calculate perimeter $P$ of the base: Since base is square with side $4$ cm, $$P = 4 \times 4 = 16 \text{ cm}$$ - Calculate lateral surface area: $$\frac{1}{2} P l = \frac{1}{2} \times 16 \times 6 = 8 \times 6 = 48 \text{ cm}^2$$ - Total surface area: $$A = B + \frac{1}{2} P l = 64 + 48 = 112 \text{ cm}^2$$ 4. **Explanation:** The base area is the area of the square base. The lateral surface area is the sum of the areas of the triangular faces, each with base equal to a side of the base and height equal to the slant height. 5. **Final answer:** The surface area of the pyramid is $112$ cm$^2$. Since multiple pyramids are shown but only the first is solved here, the count of distinct problems is 8 as per the input.