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Slant Height of Square Pyramid Formula:
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The slant height of a square pyramid is the length measured along the lateral face from the base to the apex of the square pyramid along the center of the face. It represents the true length of the triangular face from the base edge to the apex.
The calculator uses the slant height formula:
Where:
Explanation: This formula is derived from the Pythagorean theorem applied to the right triangle formed by the lateral edge, half of the base diagonal, and the slant height.
Details: Calculating the slant height is crucial for determining the surface area of the pyramid, understanding its geometric properties, and solving various architectural and engineering problems involving pyramidal structures.
Tips: Enter the lateral edge length and base edge length in meters. Both values must be positive numbers. The calculator will compute the slant height using the mathematical formula.
Q1: What is the difference between slant height and lateral edge length?
A: Slant height is measured along the face of the pyramid from base to apex, while lateral edge length is the straight line distance from a base vertex to the apex.
Q2: Can this formula be used for all square pyramids?
A: Yes, this formula applies to all right square pyramids where the apex is directly above the center of the base.
Q3: What units should I use for the measurements?
A: The calculator uses meters, but the formula works with any consistent unit of measurement (cm, mm, inches, etc.).
Q4: How accurate is the calculated slant height?
A: The calculation is mathematically exact based on the input values, with results rounded to 6 decimal places for precision.
Q5: What if I have the height instead of the lateral edge?
A: A different formula would be needed: \( h_{slant} = \sqrt{h^2 + (\frac{l_{base}}{2})^2} \), where h is the perpendicular height.