The formula to calculate the Total Surface Area of a Dodecahedron (TSA) is:
\[ TSA = 3 \sqrt{25 + (10 \sqrt{5})} \times l_e^2 \]
Where:
Total Surface Area of a Dodecahedron is the total quantity of plane enclosed by the entire surface of the Dodecahedron.
Edge Length of a Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.
Let's assume the following value:
Using the formula:
\[ TSA = 3 \sqrt{25 + (10 \sqrt{5})} \times l_e^2 \]
Evaluating:
\[ TSA = 3 \sqrt{25 + (10 \sqrt{5})} \times 10^2 \]
The Total Surface Area is 2064.5729 m².
| Edge Length (m) | Total Surface Area (m²) |
|---|---|
| 1 | 20.6457 |
| 2 | 82.5829 |
| 3 | 185.8116 |
| 4 | 330.3317 |
| 5 | 516.1432 |
| 6 | 743.2462 |
| 7 | 1,011.6407 |
| 8 | 1,321.3266 |
| 9 | 1,672.3040 |
| 10 | 2,064.5729 |