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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.

Calculate the total surface area of the following pyramid.

Learn how to calculate the total surface area of a pyramid with a square base and triangular faces. This problem involves geometry concepts, including area calculations for squares and triangles, suitable for students in Grades 7-9.

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