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

Area of Rectangle Formula:

\[ A = 4 \times r_c^2 \times \sin(\angle db) \times \cos(\angle db) \]

Area of Rectangle:

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

The formula calculates the area of a rectangle using its circumradius and the angle between the diagonal and breadth. It provides an alternative method to compute area when these specific parameters are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = 4 \times r_c^2 \times \sin(\angle db) \times \cos(\angle db) \]

Where:

\( A \) — Area of Rectangle (m²)
\( r_c \) — Circumradius of Rectangle (m)
\( \angle db \) — Angle between Diagonal and Breadth of Rectangle (rad)

Explanation: The formula utilizes trigonometric functions to relate the circumradius and angle to the area of the rectangle.

3. Importance of Area Calculation

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

4. Using the Calculator

Tips: Enter the circumradius in meters and the angle in radians. The angle should be between 0 and π/2 radians (0° to 90°).

5. Frequently Asked Questions (FAQ)

Q1: What is the circumradius of a rectangle?
A: The circumradius is the radius of the circle that passes through all four vertices of the rectangle.

Q2: How is the angle between diagonal and breadth measured?
A: The angle is measured in radians between the diagonal and the breadth (shorter side) of the rectangle.

Q3: Can this formula be used for squares?
A: Yes, since a square is a special case of a rectangle, this formula applies to squares as well.

Q4: What are the limitations of this formula?
A: The formula assumes standard geometric properties of a rectangle and may not apply to distorted or non-rectangular shapes.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, provided the input values are accurate and the rectangle conforms to the geometric assumptions.