Area of Rectangle given Perimeter and Angle between Diagonal and Breadth Calculator

Area of Rectangle Formula:

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

Area of Rectangle:

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1. What is the Area of Rectangle Formula?

The area of a rectangle can be calculated using perimeter and the angle between the diagonal and breadth. This formula provides an alternative method to find the area when these specific parameters are known.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula derives from the relationship between perimeter, area, and the trigonometric properties of rectangles.

3. Importance of Area Calculation

Details: Calculating the area of a rectangle is fundamental in geometry, architecture, engineering, and various practical applications where spatial measurements are required.

4. Using the Calculator

Tips: Enter the perimeter in meters and the angle in degrees. The angle must be between 0° and 90°. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use this formula instead of length × width?
A: This formula is useful when you know the perimeter and the angle between diagonal and breadth, but don't know the individual length and width measurements.

Q2: What is the range of valid angle values?
A: The angle must be between 0° and 90° (exclusive). At 0° or 90°, the formula becomes undefined due to trigonometric limitations.

Q3: Can this calculator handle different units?
A: The calculator uses meters for perimeter and square meters for area. You can convert other units to meters before calculation.

Q4: Are there any limitations to this formula?
A: The formula assumes a perfect rectangle and may not be accurate for quadrilaterals that deviate significantly from rectangular shape.

Q5: How precise are the results?
A: Results are calculated with high precision but rounded to 4 decimal places for practical use. The actual precision depends on the accuracy of input values.