In this article, we will guide you through the process of calculating the surface area of a tetrahedron pyramid. The surface area includes the areas of all four equilateral triangular faces of the pyramid.
Step-by-Step Guide
Step 1: Show the Surface Area Formula
The surface area (SA) of a tetrahedron pyramid can be found using the following formula:
\[ SA = \sqrt{3} \cdot a^2 \]
Where:
- \( a \) is the length of a side of the equilateral triangular faces.
Step 2: Explain the Formula
- The term \( \sqrt{3} \cdot a^2 \) represents the combined area of all four equilateral triangular faces of the tetrahedron.
Step 3: Insert Numbers as an Example
Let's consider a tetrahedron pyramid where the side length of each equilateral triangular face is:
- Side length: \( a = 5 \) units
Step 4: Calculate the Final Value
First, substitute the given side length into the surface area formula:
\[ SA = \sqrt{3} \cdot a^2 \]
\[ SA = \sqrt{3} \cdot 5^2 \]
\[ SA = \sqrt{3} \cdot 25 \]
\[ SA = 25\sqrt{3} \]
Using the approximate value of \( \sqrt{3} \approx 1.732 \):
\[ SA \approx 25 \cdot 1.732 \]
\[ SA \approx 43.3 \, \text{square units} \]
Final Value
The surface area of a tetrahedron pyramid with each side of the equilateral triangular faces measuring 5 units is approximately 43.3 square units.
