To calculate the total surface area of the given pyramid, we need to consider both the base area and the area of the triangular faces. Here's the step-by-step breakdown:

1. Identify the shape and dimensions:

• The base of the pyramid is a square with each side measuring $5 \, \text{cm}$.
• The slant height of each triangular face is $4 \, \text{cm}$.

2. Calculate the area of the base:

Since the base is a square: $\text{Area of the base} = \text{side}^2 = 5 \times 5 = 25 \, \text{cm}^2$

3. Calculate the area of one triangular face:

Each triangular face has:

• A base of $5 \, \text{cm}$ (same as the side of the square base).
• A slant height of $4 \, \text{cm}$.

The area of one triangular face is: $\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 4 = 10 \, \text{cm}^2$

4. Calculate the total area of the triangular faces:

There are four triangular faces, so: $\text{Total area of triangular faces} = 4 \times 10 = 40 \, \text{cm}^2$

5. Calculate the total surface area of the pyramid:

$\text{Total surface area} = \text{Area of the base} + \text{Total area of triangular faces} = 25 + 40 = 65 \, \text{cm}^2$

Answer:

The total surface area of the pyramid is: $65 \, \text{cm}^2$

Would you like further details or have any questions?

Here are some related questions for practice:

1. How would the surface area change if the side of the base were increased to 6 cm?
2. What is the total surface area if the slant height were 5 cm instead of 4 cm?
3. How do you calculate the volume of this pyramid?
4. How would the surface area change if the pyramid had a rectangular base instead of a square base?
5. Can you calculate the lateral surface area only (excluding the base)?

Tip: Always check if the pyramid’s base is a square or rectangle, as this impacts the area calculations.