Area of Cut Rectangle Given Slant Side Calculator

Formula Used:

\[ A = (S_{Long} \times S_{Short}) - \frac{\sqrt{S_{Slant}^2 - (S_{Short} - S_{Short\ Cut})^2} \times (S_{Short} - S_{Short\ Cut})}{2} \]

Long Rectangle Side (S_Long):

Short Rectangle Side (S_Short):

Slant Side (S_Slant):

Short Cut Side (S_{Short Cut}):

Area of Cut Rectangle (A):

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1. What is the Area of Cut Rectangle?

The Area of Cut Rectangle is the total quantity of plane enclosed by the boundary of the Cut Rectangle. It represents the remaining area after a portion has been removed from a rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = (S_{Long} \times S_{Short}) - \frac{\sqrt{S_{Slant}^2 - (S_{Short} - S_{Short\ Cut})^2} \times (S_{Short} - S_{Short\ Cut})}{2} \]

Where:

\( A \) — Area of Cut Rectangle (m²)
\( S_{Long} \) — Long Rectangle Side (m)
\( S_{Short} \) — Short Rectangle Side (m)
\( S_{Slant} \) — Slant Side of Cut Rectangle (m)
\( S_{Short\ Cut} \) — Short Cut Side of Cut Rectangle (m)

Explanation: The formula calculates the area by subtracting the area of the removed triangular portion from the original rectangle's area.

3. Importance of Area Calculation

Details: Calculating the area of cut rectangles is important in various fields including architecture, engineering, and manufacturing where precise area measurements are needed for materials estimation and design purposes.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure that the slant side is longer than the difference between the short side and short cut side for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a Cut Rectangle?
A: A Cut Rectangle is a geometric shape formed by removing a right-angled triangular portion from a rectangle.

Q2: What units should I use for measurements?
A: The calculator uses meters, but you can use any consistent unit as long as all measurements are in the same unit.

Q3: What if the slant side is too short?
A: The calculation requires that the slant side must be longer than the difference between the short side and short cut side. Otherwise, the square root calculation would involve a negative number.

Q4: Can the short cut side be equal to the short side?
A: No, the short cut side must be less than the short side; otherwise, there would be no cut portion.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the inputs provided. The accuracy depends on the precision of your measurements.