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The formula calculates the vertical height of a square pyramid when the slant height and base edge length are known. It's derived from the Pythagorean theorem applied to the right triangle formed by the height, slant height, and half the diagonal of the base.
The calculator uses the formula:
Where:
Explanation: The formula applies the Pythagorean theorem where the slant height is the hypotenuse, the height is one leg, and half the base diagonal is the other leg.
Details: Calculating the height of a square pyramid is essential in geometry, architecture, and construction for determining volume, surface area, and structural properties of pyramidal shapes.
Tips: Enter slant height and base edge length in meters. Both values must be positive numbers. The calculator will compute the vertical height of the pyramid.
Q1: What is the difference between slant height and vertical height?
A: Slant height is the distance along the lateral face from base to apex, while vertical height is the perpendicular distance from base to 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 if my pyramid has a rectangular base?
A: This formula is specific to square pyramids. For rectangular pyramids, a different formula involving both length and width is needed.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact when accurate measurements are provided, following geometric principles.
Q5: What units should I use for the inputs?
A: The calculator uses meters, but any consistent unit can be used as long as all inputs are in the same unit.