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To solve this problem, we need to find the sum of all the edges of the pyramid. Let's analyze the given information:

1. **The base of the pyramid is a square.**  
   This means the base has 4 edges, each forming the sides of the square.

2. **Each triangular face is an equilateral triangle with a perimeter of 30 cm.**  
   Since each triangular face is equilateral, all three sides of the triangle are equal. Thus, the length of each side of the equilateral triangle is:
   \[
   \text{Side length} = \frac{30}{3} = 10 \text{ cm}.
   \]

3. **Edges of the pyramid:**
   - The base of the pyramid has 4 edges, each with a length of 10 cm.
   - The pyramid has 4 lateral edges connecting the apex to each vertex of the square base. Each of these edges corresponds to a side of one of the equilateral triangles, so each of these edges is also 10 cm long.

4. **Calculating the total edge length:**
   \[
   \text{Sum of all edges} = (4 \times 10) + (4 \times 10) = 40 + 40 = 80 \text{ cm}.
   \]

Therefore, the sum of the lengths of all the edges of the pyramid is **80 cm**.

Would you like a more detailed explanation or have any questions?

Here are some related questions you might find interesting:
1. How do we calculate the surface area of this pyramid?
2. What is the volume of a square pyramid given the height?
3. How does the type of base affect the calculation of the edges in different pyramids?
4. What changes if the triangular faces are not equilateral?
5. How would the edge lengths change if the perimeter of the triangular face was different?

**Tip:** When dealing with geometric shapes, always visualize or sketch the figure. This helps in identifying relationships between edges, faces, and vertices.

The base of a pyramid is a square. Each triangular face of the pyramid is an equilateral triangle with a perimeter of 30 cm. What is the sum of the lengths of all the edges of the pyramid?

Learn how to calculate the sum of the lengths of all edges of a pyramid where the base is a square, and the triangular faces are equilateral with a perimeter of 30 cm. This problem covers key geometry concepts, including perimeter formulas and understanding of 3D shapes.

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