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 length. This provides an alternative method to the standard length × width calculation.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A \) — Area of Rectangle (m²)
• \( D_c \) — Diameter of Circumcircle of Rectangle (m)
• \( \angle_{dl} \) — Angle between Diagonal and Length of Rectangle (rad)

Explanation: This formula derives from trigonometric relationships between the rectangle's diagonal (equal to the circumcircle diameter), the angle with the length, and the resulting area.

3. Importance of Rectangle Area Calculation

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

4. Using the Calculator

Tips: Enter the circumcircle diameter in meters and the angle in radians. The angle must be between 0 and π/2 radians (0-90 degrees).

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, but not the direct length and width measurements.

Q2: What is the range of valid angle values?
A: The angle must be between 0 and π/2 radians (0-90 degrees) as it represents an angle within a 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 rectangle's diagonal length.

Q4: Can this formula be used for squares?
A: Yes, for squares the angle between diagonal and length is π/4 radians (45 degrees), and the formula simplifies accordingly.

Q5: What units should be used for inputs?
A: Diameter in meters, angle in radians. Ensure consistent units for accurate results.