1. What is the Area of Rectangle Formula?

The area of a rectangle given its breadth and the angle between the diagonal and length is calculated using the formula: \( A = b^2 \times \cot(\angle_{dl}) \), where \( b \) is the breadth and \( \angle_{dl} \) is the angle between the diagonal and length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area of the rectangle (m²)
• \( b \) — Breadth of the rectangle (m)
• \( \angle_{dl} \) — Angle between diagonal and length (radians)
• \( \cot \) — Cotangent trigonometric function

Explanation: This formula derives from the relationship between the sides of the rectangle and the angle between the diagonal and the length side.

3. Importance of Area Calculation

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

4. Using the Calculator

Tips: Enter the breadth in meters and the angle in radians. Both values must be positive numbers (breadth > 0, angle > 0).

5. Frequently Asked Questions (FAQ)

Q1: Why use radians instead of degrees for the angle?
A: Trigonometric functions in mathematical calculations typically use radians. If you have degrees, convert them to radians first (radians = degrees × π/180).

Q2: What is the range of valid angle values?
A: The angle should be between 0 and π/2 radians (0-90 degrees) for a valid rectangle.

Q3: How is the cotangent function calculated?
A: Cotangent is the reciprocal of tangent: cot(θ) = 1/tan(θ) = adjacent/opposite.

Q4: Can this formula be used for squares?
A: Yes, since a square is a special case of rectangle where all sides are equal.

Q5: What if I know the length instead of breadth?
A: There's an alternative formula using length: \( A = l^2 \times \tan(\angle_{dl}) \), where l is the length.