Area of Rectangle Given Perimeter and Angle Between Diagonal and Length Calculator

Formula Used:

\[ \text{Area of Rectangle} = \frac{(P/2)^2}{(\tan(\angle_{dl}) + 1) \cdot (\cot(\angle_{dl}) + 1)} \]

Area of Rectangle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Area of Rectangle Formula?

The area of a rectangle given its perimeter and the angle between the diagonal and length is calculated using a specialized trigonometric formula that relates these parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = \frac{(P/2)^2}{(\tan(\angle_{dl}) + 1) \cdot (\cot(\angle_{dl}) + 1)} \]

Where:

\( A \) — Area of Rectangle (m²)
\( P \) — Perimeter of Rectangle (m)
\( \angle_{dl} \) — Angle between Diagonal and Length of Rectangle (degrees)
\( \tan \) — Tangent trigonometric function
\( \cot \) — Cotangent trigonometric function

Explanation: This formula derives from the geometric relationships between a rectangle's perimeter, the angle its diagonal makes with its length, and its area.

3. Importance of Area Calculation

Details: Calculating the area of a rectangle is fundamental in geometry and has practical applications in construction, land measurement, packaging, and various engineering fields.

4. Using the Calculator

Tips: Enter the perimeter in meters and the angle in degrees (between 0 and 90). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula?
A: This formula provides a direct way to calculate area when you know the perimeter and the angle between the diagonal and length, without needing to find individual side lengths.

Q2: What is the range of valid angle values?
A: The angle must be between 0° and 90° (exclusive). At 0° or 90°, the rectangle degenerates into special cases.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact, though practical accuracy depends on the precision of your input measurements.

Q4: Can this formula be used for squares?
A: Yes, for a square (where angle is 45°), the formula correctly calculates the area.

Q5: What units should I use?
A: Use consistent units (meters for perimeter gives square meters for area). The calculator assumes metric units but the formula works with any consistent unit system.