https://file.aiquickdraw.com/mathbot/file/1726081314922w98fz2rs.jpg

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.

What is the lateral surface area of a triangular pyramid?

Learn how to calculate the lateral surface area of a triangular pyramid with a base of 4 mm and a height of 3 mm. This problem involves understanding geometry concepts like the area of triangles and surface areas of solids. Suitable for students in Grades 6-8.

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