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

Formula Used:

\[ A = D_c^2 \times \sin(\angle_{db}) \times \cos(\angle_{db}) \]

Area of Rectangle:

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1. What is the Area of Rectangle Formula?

The formula calculates the area of a rectangle using the diameter of its circumcircle and the angle between the diagonal and breadth. This approach provides an alternative method to calculate area using geometric properties of the rectangle and its circumscribed circle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = D_c^2 \times \sin(\angle_{db}) \times \cos(\angle_{db}) \]

Where:

\( A \) — Area of Rectangle (m²)
\( D_c \) — Diameter of Circumcircle of Rectangle (m)
\( \angle_{db} \) — Angle between Diagonal and Breadth of Rectangle (degrees)

Explanation: The formula leverages trigonometric relationships between the rectangle's diagonal (which equals the circle's diameter), the angle between the diagonal and breadth, and the resulting area calculation.

3. Importance of Area Calculation

Details: Calculating the area of a rectangle is fundamental in geometry, architecture, engineering, and various practical applications. This specific formula provides an alternative approach when the circumcircle diameter and angle information are available.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle in meters and the angle between the diagonal and breadth in degrees (0-90°). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use this formula instead of length × width?
A: This formula is useful when you know the circumcircle properties and the angle between diagonal and breadth, but don't have direct measurements of length and width.

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 circumcircle related to the rectangle?
A: The circumcircle of a rectangle passes through all four vertices, and its diameter equals the length of the rectangle's diagonal.

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 the practical applications of this calculation?
A: This calculation is useful in geometric design, architectural planning, and engineering applications where circular and rectangular elements interact.