Area Of Rectangle Given Breadth And Acute Angle Between Diagonals Calculator

Formula Used:

\[ A = b^2 \times \cot\left(\frac{\theta}{2}\right) \]

Area of Rectangle:

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1. What is the Area of Rectangle Formula?

The area of a rectangle can be calculated using the formula \( A = b^2 \times \cot(\theta/2) \), where \( b \) is the breadth of the rectangle and \( \theta \) is the acute angle between its diagonals. This formula provides an alternative method to calculate area when the breadth and diagonal angle are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = b^2 \times \cot\left(\frac{\theta}{2}\right) \]

Where:

\( A \) — Area of the rectangle (m²)
\( b \) — Breadth of the rectangle (m)
\( \theta \) — Acute angle between diagonals (degrees)
\( \cot \) — Cotangent trigonometric function

Explanation: The formula derives from the geometric relationship between the rectangle's dimensions and the angle between its diagonals, using trigonometric identities to express area in terms of breadth and diagonal angle.

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 where rectangular shapes are involved.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why use this formula instead of length × breadth?
A: This formula is useful when you know the breadth and the angle between diagonals but not the length of the rectangle.

Q2: What is the range of valid angle values?
A: The acute angle between diagonals must be between 0 and 90 degrees (exclusive) for a proper rectangle.

Q3: How is the cotangent function calculated?
A: The cotangent is calculated as the reciprocal of the tangent function: \( \cot(x) = 1/\tan(x) \).

Q4: Can this formula be used for squares?
A: Yes, for squares (where breadth equals length), the acute angle between diagonals is always 90 degrees, and the formula simplifies accordingly.

Q5: What units should be used for inputs?
A: Breadth should be in meters, and angle should be in degrees. The resulting area will be in square meters.