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

Area of Rectangle Formula:

\[ A = \frac{d^2 \times \sin(2 \times \angle db)}{2} \]

Area of Rectangle:

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1. What is the Area of Rectangle given Diagonal and Angle Formula?

The area of a rectangle can be calculated using the diagonal length and the angle between the diagonal and the breadth. This formula provides an alternative method to the traditional length × width calculation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = \frac{d^2 \times \sin(2 \times \angle db)}{2} \]

Where:

\( A \) — Area of Rectangle (m²)
\( d \) — Diagonal of Rectangle (m)
\( \angle db \) — Angle between Diagonal and Breadth of Rectangle (radians)

Explanation: The formula utilizes trigonometric relationships between the diagonal, angle, and sides of the rectangle to calculate the area.

3. Importance of Rectangle Area Calculation

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

4. Using the Calculator

Tips: Enter the diagonal length in meters and the angle in degrees between the diagonal and breadth. The angle must be between 0° and 90°.

5. Frequently Asked Questions (FAQ)

Q1: Why use this formula instead of length × width?
A: This formula is useful when you know the diagonal and angle but not the individual side lengths of the rectangle.

Q2: What is the range of valid angle values?
A: The angle between diagonal and breadth must be between 0° and 90° for a valid rectangle.

Q3: How is the angle converted from degrees to radians?
A: The calculator automatically converts degrees to radians using the formula: radians = degrees × π/180.

Q4: Can this formula be used for squares?
A: Yes, for squares the angle between diagonal and breadth is 45°, and the formula simplifies accordingly.

Q5: What are practical applications of this calculation?
A: This calculation is useful in construction, carpentry, graphic design, and any field where rectangular areas need to be determined from diagonal measurements.