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Height Formula:
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The height formula for a square-based pyramid calculates the perpendicular height from the apex to the base center using the slant height and base length. This is derived from the Pythagorean theorem applied to the right triangle formed by the height, half the base, and the slant height.
The calculator uses the formula:
Where:
Explanation: The formula applies the Pythagorean theorem to the right triangle formed by the height (h), half the base (b/2), and the slant height (s), where \( h^2 = s^2 - (b/2)^2 \).
Details: Calculating the height of a square-based pyramid is essential in geometry, architecture, and engineering for determining volume, surface area, and structural properties of pyramidal shapes.
Tips: Enter the slant height and base length in consistent units. Both values must be positive numbers. The calculator will compute the perpendicular height from the apex to the base center.
Q1: What's the difference between slant height and height?
A: Slant height is the distance from the apex to the midpoint of a base edge, while height is the perpendicular distance from the apex to the center of the base.
Q2: Can this formula be used for rectangular pyramids?
A: No, this specific formula applies only to square-based pyramids where all base sides are equal. For rectangular pyramids, a different approach is needed.
Q3: What if the slant height is less than half the base?
A: Mathematically, this would result in a negative value under the square root, indicating an impossible pyramid configuration with the given measurements.
Q4: How accurate is this calculation?
A: The calculation is mathematically precise when correct measurements are provided, following the principles of Euclidean geometry.
Q5: Can I calculate volume using this height?
A: Yes, once you have the height, you can calculate volume using the formula: \( Volume = \frac{1}{3} \times base^2 \times height \).