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The Height of Truncated Square is the total distance between the lowest and highest points of the Truncated Square. It is an important geometric measurement used in various mathematical and engineering applications.
The calculator uses the formula:
Where:
Explanation: This formula is derived from the Pythagorean theorem, where the height forms one leg of a right triangle with the diagonal as hypotenuse and half the side as the other leg.
Details: Accurate height calculation is crucial for determining the geometric properties of truncated squares, which are used in architectural design, engineering applications, and various mathematical problems involving geometric shapes.
Tips: Enter the diagonal and side values in meters. Both values must be positive numbers, and the diagonal must be greater than the side for a valid calculation.
Q1: What is a Truncated Square?
A: A Truncated Square is a geometric shape formed by cutting off the corners of a square, resulting in an octagon with alternating long and short sides.
Q2: Why is the diagonal always longer than the side?
A: In any polygon, the diagonal connecting non-adjacent vertices is always longer than any single side due to the triangle inequality theorem.
Q3: Can this formula be used for other polygons?
A: This specific formula applies to truncated squares. Other polygons have different geometric relationships between their diagonals, sides, and heights.
Q4: What if the diagonal equals the side?
A: If diagonal equals side, the height would be zero, which is not possible for a valid truncated square. This indicates invalid input values.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using precise input values. The result's practical accuracy depends on the precision of the input measurements.