Area of Cut Rectangle Given Perimeter and Long Rectangle Side Calculator

Formula Used:

\[ Area = (S_{Long} \times S_{Short}) - \frac{(S_{Long} - (P - (S_{Long} + S_{Short} + S_{Short\ Cut} + S_{Slant}))) \times (S_{Short} - S_{Short\ Cut})}{2} \]

Long Rectangle Side (S_Long):

Short Rectangle Side (S_Short):

Perimeter (P):

Short Cut Side (S_{Short Cut}):

Slant Side (S_Slant):

Area of Cut Rectangle:

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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 removing a cut portion from a rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Area = (S_{Long} \times S_{Short}) - \frac{(S_{Long} - (P - (S_{Long} + S_{Short} + S_{Short\ Cut} + S_{Slant}))) \times (S_{Short} - S_{Short\ Cut})}{2} \]

Where:

\( S_{Long} \) — Long Rectangle Side of Cut Rectangle (m)
\( S_{Short} \) — Short Rectangle Side of Cut Rectangle (m)
\( P \) — Perimeter of Cut Rectangle (m)
\( S_{Short\ Cut} \) — Short Cut Side of Cut Rectangle (m)
\( S_{Slant} \) — Slant 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: Accurate area calculation is crucial for various applications including construction, manufacturing, and geometric analysis where cut rectangles are involved.

4. Using the Calculator

Tips: Enter all dimensions in meters. Ensure all values are positive and valid. The perimeter must be greater than the sum of all sides.

5. Frequently Asked Questions (FAQ)

Q1: What is a Cut Rectangle?
A: A Cut Rectangle is a geometric shape formed by removing a triangular portion from a rectangle, resulting in a five-sided polygon.

Q2: When is this calculation useful?
A: This calculation is useful in construction, carpentry, manufacturing, and any field where materials are cut from rectangular shapes.

Q3: What are the constraints for valid inputs?
A: All dimensions must be positive, and the perimeter must be greater than the sum of the four given sides (SLong + SShort + SShort Cut + SSlant).

Q4: Can this formula handle different units?
A: The formula works with any consistent unit system, but all inputs must be in the same units (meters in this calculator).

Q5: What if the calculated area is negative?
A: A negative area indicates invalid input values where the cut portion would be larger than the original rectangle, which is geometrically impossible.