The formula to calculate the Height of Square Pyramid (h) is:
\[ h = \sqrt{\left(\frac{TSA - le(Base)^2}{le(Base)}\right)^2 - le(Base)^2 \over 4} \]
Where:
The Height of Square Pyramid is the length of the perpendicular from the apex to the base of the Square Pyramid.
Total Surface Area of Square Pyramid is the total amount of two-dimensional space occupied on all the faces of the Square Pyramid.
Edge Length of Base of Square Pyramid is the length of the straight line connecting any two adjacent vertices of the base of the Square Pyramid.
Let's assume the following values:
Using the formula:
\[ h = \sqrt{\left(\frac{420 - 10^2}{10}\right)^2 - 10^2 \over 4} \]
Evaluating:
\[ h \approx 15.1986841535707 \]
The Height of Square Pyramid is approximately 15.1986841535707 Meters.
| Total Surface Area (TSA) (Square Meters) | Edge Length (le(Base)) (Meters) | Height (h) (Meters) |
|---|---|---|
| 300 | 8 | 14.197270864501 |
| 300 | 10 | 8.660254037844 |
| 300 | 12 | 2.500000000000 |
| 420 | 8 | 21.887496430611 |
| 420 | 10 | 15.198684153571 |
| 420 | 12 | 9.810708435174 |
| 500 | 8 | 26.954823316060 |
| 500 | 10 | 19.364916731037 |
| 500 | 12 | 13.565683830083 |