The formula to calculate the Total Surface Area of a Pyramid is:
\[ \text{TSA} = \text{le(Base)}^2 + \left( \text{le(Base)} \times \sqrt{(4h^2) + \text{le(Base)}^2} \right) \]
Where:
The Total Surface Area of a Pyramid is the total amount of two-dimensional space occupied by all the faces of the Pyramid.
Let's assume the following values:
Using the formula:
\[ \text{TSA} = 10^2 + \left( 10 \times \sqrt{(4 \times 15^2) + 10^2} \right) \]
Evaluating:
\[ \text{TSA} = 416.227766016838 \]
The Total Surface Area of the Pyramid is approximately 416.23 square meters.
| Edge Length of Base (meters) | Height of Pyramid (meters) | Total Surface Area (square meters) |
|---|---|---|
| 5 | 10 | 128.077640640442 |
| 5 | 12 | 147.576506721313 |
| 5 | 14 | 167.214626533279 |
| 5 | 16 | 186.941347407016 |
| 5 | 18 | 206.727818453862 |
| 5 | 20 | 226.556443707464 |
| 7 | 10 | 197.327340702920 |
| 7 | 12 | 224.000000000000 |
| 7 | 14 | 251.032175655265 |
| 7 | 16 | 278.296750958229 |
| 7 | 18 | 305.719691492492 |
| 7 | 20 | 333.255167059457 |
| 9 | 10 | 278.385409795152 |
| 9 | 12 | 311.688101123573 |
| 9 | 14 | 345.697941057349 |
| 9 | 16 | 380.173862494704 |
| 9 | 18 | 414.971555675031 |
| 9 | 20 | 450.000000000000 |
| 11 | 10 | 372.079668631293 |
| 11 | 12 | 411.408333213770 |
| 11 | 14 | 451.915397042809 |
| 11 | 16 | 493.216334945150 |
| 11 | 18 | 535.073664943812 |
| 11 | 20 | 577.334307279214 |
| 13 | 10 | 479.098371488791 |
| 13 | 12 | 523.830945662861 |
| 13 | 14 | 570.319075051261 |
| 13 | 16 | 618.017817018434 |
| 13 | 18 | 666.579139434121 |
| 13 | 20 | 715.773261965140 |
| 15 | 10 | 600.000000000000 |
| 15 | 12 | 649.529150942547 |
| 15 | 14 | 701.471405228058 |
| 15 | 16 | 755.117911412169 |
| 15 | 18 | 810.000000000000 |
| 15 | 20 | 865.800280898815 |