1. What is the Area of Rectangle Formula?

The area of a rectangle given its perimeter and acute angle between diagonals is calculated using a specialized trigonometric formula that relates these geometric properties.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula derives from the relationship between a rectangle's perimeter, the angle between its diagonals, and its area using trigonometric identities.

3. Importance of Area Calculation

Details: Calculating the area of a rectangle is fundamental in geometry, architecture, engineering, and various practical applications where rectangular shapes are involved.

4. Using the Calculator

Tips: Enter the perimeter in meters and the acute angle between diagonals in degrees. The angle must be between 0 and 90 degrees, and the perimeter must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid angle values?
A: The acute angle between diagonals must be between 0 and 90 degrees (0° < θ < 90°).

Q2: Can this formula be used for squares?
A: Yes, squares are a special case of rectangles where all sides are equal and the acute angle between diagonals is 90 degrees.

Q3: What units should I use for inputs?
A: Perimeter should be in meters, and angle should be in degrees. The area result will be in square meters.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values, using trigonometric functions for computation.

Q5: Can I use this for other quadrilateral shapes?
A: No, this formula is specifically derived for rectangles and may not apply to other quadrilateral shapes.