The formula to calculate the Total Surface Area of an Icosahedron (TSA) is:
\[ TSA = 5 \sqrt{3} \times l_e^2 \]
Where:
Total Surface Area of an Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron.
Edge Length of an Icosahedron is the length of any of the edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.
Let's assume the following value:
Using the formula:
\[ TSA = 5 \sqrt{3} \times l_e^2 \]
Evaluating:
\[ TSA = 5 \sqrt{3} \times 10^2 \]
The Total Surface Area is 866.0254 m².
| Edge Length (m) | Total Surface Area (m²) |
|---|---|
| 1 | 8.6603 |
| 2 | 34.6410 |
| 3 | 77.9423 |
| 4 | 138.5641 |
| 5 | 216.5064 |
| 6 | 311.7691 |
| 7 | 424.3524 |
| 8 | 554.2563 |
| 9 | 701.4806 |
| 10 | 866.0254 |