To find the surface area of the square-based pyramid, we need to calculate the area of its base and the area of its four triangular sides.

Given:

1. Base side length (s): 6 cm
2. Slant height of the pyramid (l): 5 cm

Step-by-step Solution:

1. Area of the Base: The base is a square, so the area of the base (A_base) is: $A_{\text{base}} = s^2 = 6 \times 6 = 36 \, \text{cm}^2$

2. Area of the Triangular Sides: Each of the four triangular sides has a base equal to the side of the square (6 cm) and a slant height of 5 cm.

   The area of one triangular side (A_triangle) is: $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 6 \times 5 = 15 \, \text{cm}^2$

   Since there are four triangular sides, the total area of the triangles (A_triangles_total) is: $A_{\text{triangles total}} = 4 \times 15 = 60 \, \text{cm}^2$

3. Total Surface Area: The total surface area of the pyramid (A_total) is the sum of the area of the base and the total area of the triangular sides: $A_{\text{total}} = A_{\text{base}} + A_{\text{triangles total}} = 36 + 60 = 96 \, \text{cm}^2$

Final Answer:

The surface area of the square-based pyramid is 96 square centimeters.

Would you like further details, or do you have any questions?

Here are some related questions you might find interesting:

1. How would the surface area change if the slant height were increased to 7 cm?
2. What would the surface area be if the base side length were doubled?
3. How do you find the volume of a square-based pyramid?
4. What is the difference between the slant height and the perpendicular height of a pyramid?
5. How does the surface area formula change for a pyramid with a rectangular base?

Tip: To find the surface area of any pyramid, always calculate the base area and add it to the total area of all its triangular sides.