https://file.aiquickdraw.com/mathbot/file/1727369107501svo2nmet.jpg

The image shows a triangular pyramid (tetrahedron) with the following details:

- All faces of the pyramid are equilateral triangles.
- The base of the pyramid has a side length of 78 cm.
- The height of one of the triangular faces is 80 cm.

To find the surface area of the pyramid, we need to calculate the area of all four equilateral triangles that make up the surface of the pyramid.

### Step 1: Area of one equilateral triangle
The area \( A \) of an equilateral triangle can be calculated using the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Given:
- Base = 78 cm
- Height = 80 cm

\[
A = \frac{1}{2} \times 78 \, \text{cm} \times 80 \, \text{cm}
\]

### Step 2: Total Surface Area
Since the pyramid has 4 equilateral triangular faces, the total surface area \( S \) is:
\[
S = 4 \times A
\]

Let me calculate that.The total surface area of the triangular pyramid is 12,480 cm².

Would you like more details, or do you have any further questions?

Here are 5 related questions to explore:
1. How is the volume of a pyramid calculated?
2. What are the properties of an equilateral triangle?
3. How does surface area change if the height of the triangle changes?
4. How can the lateral surface area of a pyramid be calculated?
5. What is the difference between a triangular pyramid and other pyramids?

**Tip:** Surface area calculations involve summing the areas of all faces, so knowing the shape of each face is crucial.

All the triangles in this triangular pyramid have the same measures. What is the surface area of the pyramid?

Learn how to calculate the surface area of a triangular pyramid where all faces are equilateral triangles. Given a base length of 78 cm and a height of 80 cm, we walk through the steps to compute the total surface area.

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