The formula to calculate the Height of a Triangular Prism given the Lateral Surface Area is:
\[ h = \frac{\text{LSA}}{S_a + S_b + S_c} \]
The height of a triangular prism is the length of the straight line connecting any base vertex to the corresponding top vertex of the prism. The lateral surface area is the quantity of plane enclosed by all the lateral surfaces (excluding the top and bottom faces) of the prism. The sides A, B, and C are the lengths of the three base edges.
Let's assume the following values:
Using the formula:
\[ h = \frac{1100}{10 + 14 + 20} = 25 \]
The Height is 25 Meters.
| Lateral Surface Area (Square Meters) | Side A (Meters) | Side B (Meters) | Side C (Meters) | Height (Meters) |
|---|---|---|---|---|
| 1050 | 10 | 14 | 20 | 23.863636363636363 |
| 1100 | 10 | 14 | 20 | 25.000000000000000 |
| 1150 | 10 | 14 | 20 | 26.136363636363637 |