The formula to calculate the Total Surface Area of Icosahedron is:
\[ TSA = 5 \cdot \sqrt{3} \cdot \left( \frac{4 \cdot rc}{\sqrt{10 + 2\sqrt{5}}} \right)^2 \]
Total Surface Area of Icosahedron is the total quantity of plane enclosed by the entire surface of the Icosahedron. Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.
Let's assume the following values:
Using the formula:
\[ TSA = 5 \cdot \sqrt{3} \cdot \left( \frac{4 \cdot 9}{\sqrt{10 + 2\sqrt{5}}} \right)^2 = 775.537852045189 \]
The Total Surface Area is 775.537852045189 Square Meters.
| Circumsphere Radius (Meters) | Total Surface Area (Square Meters) |
|---|---|
| 8 | 612.770648529531968 |
| 8.5 | 691.760614941542030 |
| 9 | 775.537852045189084 |
| 9.5 | 864.102359840473014 |
| 10 | 957.454138327394048 |