The image shows a triangular pyramid (tetrahedron) with given dimensions: a height of 3 mm for each triangular face, and a base of 4 mm.

To find the lateral surface area of this pyramid, we consider the sum of the areas of its triangular faces (since there are four triangular faces in a tetrahedron). Each triangular face has a base of 4 mm and a height of 3 mm.

The area $A$ of one triangular face is calculated by the formula:

$A = \frac{1}{2} \times \text{base} \times \text{height}$

Substituting the values:

$A = \frac{1}{2} \times 4 \, \text{mm} \times 3 \, \text{mm} = 6 \, \text{mm}^2$

Since the pyramid has 4 identical triangular faces, the lateral surface area $A_\text{lateral}$ is:

$A_\text{lateral} = 4 \times 6 \, \text{mm}^2 = 24 \, \text{mm}^2$

Thus, the lateral surface area of the pyramid is 24 mm².

Do you need further details or have any questions?

Here are some related questions for further exploration:

1. What is the total surface area of the pyramid, including the base?
2. How do we calculate the volume of a pyramid with the given dimensions?
3. What would the lateral surface area be if the height of each triangular face increased?
4. Can you calculate the lateral surface area for a square pyramid?
5. How would the lateral surface area change if the base were doubled?

Tip: In geometry, "lateral surface area" excludes the base and focuses only on the sides of a 3D shape.