Area of Truncated Square given Diagonal, Height and Missing Length Calculator

Formula Used:

\[ A = (\sqrt{d^2 - h^2} + 2 \times l_{Missing})^2 - 2 \times l_{Missing}^2 \]

Diagonal of Truncated Square:

Height of Truncated Square:

Missing Length of Truncated Square:

Area of Truncated Square:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Area of Truncated Square?

The Area of Truncated Square is the amount of space occupied by a Truncated Square in the given plane. A truncated square is a square with its corners cut off, creating a shape with eight sides.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = (\sqrt{d^2 - h^2} + 2 \times l_{Missing})^2 - 2 \times l_{Missing}^2 \]

Where:

\( A \) — Area of Truncated Square (m²)
\( d \) — Diagonal of Truncated Square (m)
\( h \) — Height of Truncated Square (m)
\( l_{Missing} \) — Missing Length of Truncated Square (m)

Explanation: This formula calculates the area by first finding the base dimension using the Pythagorean theorem with the diagonal and height, then accounting for the missing corner sections.

3. Importance of Area Calculation

Details: Calculating the area of truncated squares is important in various fields including architecture, engineering, and design where this shape is commonly used in floor plans, structural elements, and decorative patterns.

4. Using the Calculator

Tips: Enter the diagonal, height, and missing length in meters. All values must be positive numbers. The missing length represents the measurement of the cut-off corners.

5. Frequently Asked Questions (FAQ)

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 octagonal shape with four longer sides and four shorter sides.

Q2: How accurate is this calculation?
A: The calculation is mathematically precise when accurate measurements are provided. The result is limited only by the precision of the input values.

Q3: Can this formula be used for any truncated square?
A: Yes, this formula works for any truncated square where the corners are cut off symmetrically and the missing lengths are equal on all sides.

Q4: What units should I use for the inputs?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as long as all measurements are in the same unit.

Q5: How is the diagonal measured in a truncated square?
A: The diagonal is measured between two opposite vertices of the truncated square, passing through the center of the shape.