Area of Rectangle given Perimeter and Obtuse Angle between Diagonals Calculator

Formula Used:

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

Area of Rectangle:

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1. What is the Area of Rectangle Formula?

This calculator computes the area of a rectangle using its perimeter and the obtuse angle between its diagonals. The formula accounts for the geometric relationship between these parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( A \) — Area of Rectangle (m²)
\( P \) — Perimeter of Rectangle (m)
\( \theta \) — Obtuse Angle between Diagonals (degrees)
\( \tan \) — Tangent trigonometric function
\( \cot \) — Cotangent trigonometric function

Explanation: The formula derives from the geometric properties of rectangles and trigonometric relationships between sides and diagonals.

3. Importance of Rectangle Area Calculation

Details: Calculating rectangle area is fundamental in geometry, architecture, engineering, and various practical applications involving rectangular spaces and surfaces.

4. Using the Calculator

Tips: Enter perimeter in meters, obtuse angle in degrees (must be between 90° and 180°). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why is the angle restricted to obtuse angles?
A: In a rectangle, the diagonals always create one acute and one obtuse angle. The obtuse angle is used in this specific formula derivation.

Q2: What if I know the acute angle instead?
A: The acute angle can be calculated as (180° - obtuse angle). You can convert and use the obtuse angle value.

Q3: Are there other ways to calculate rectangle area?
A: Yes, area can also be calculated as length × width, or using diagonals and the angle between them.

Q4: What units should I use?
A: Use consistent units. The calculator expects perimeter in meters and returns area in square meters.

Q5: Can this formula be used for squares?
A: Yes, squares are special rectangles. For squares, the angle between diagonals is always 90°.