1. What is the Perimeter of Equilateral Triangle given Circumradius?

The perimeter of an equilateral triangle can be calculated from its circumradius using the formula: P = 3 × √3 × r_c, where r_c is the circumradius. This formula provides the total length around the equilateral triangle when the radius of its circumscribed circle is known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( P \) — Perimeter of Equilateral Triangle (m)
• \( r_c \) — Circumradius of Equilateral Triangle (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula establishes a direct relationship between the circumradius and the perimeter of an equilateral triangle, utilizing the mathematical constant √3.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter from circumradius is essential in geometry problems, construction planning, and various engineering applications where the circumradius is known but the perimeter is required.

4. Using the Calculator

Tips: Enter the circumradius value in meters. The value must be positive and valid (circumradius > 0).

5. Frequently Asked Questions (FAQ)

Q1: Why is there a √3 in the formula?
A: The √3 factor comes from the geometric relationship between the circumradius and side length in an equilateral triangle.

Q2: What are typical circumradius values for equilateral triangles?
A: Circumradius values vary depending on the size of the triangle. For a triangle with side length 'a', the circumradius is a/√3.

Q3: Can this formula be used for other types of triangles?
A: No, this specific formula applies only to equilateral triangles where all sides and angles are equal.

Q4: What are the units for the result?
A: The perimeter result will be in the same units as the input circumradius (typically meters).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and proper implementation of the square root function.