1. What is the Circumradius of Equilateral Triangle?

The circumradius of an equilateral triangle is the radius of the circumscribed circle that passes through all three vertices of the triangle. For an equilateral triangle, this radius is directly related to the side length and perimeter of the triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The formula derives from the relationship between the side length and circumradius of an equilateral triangle, where the perimeter is three times the side length.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry, engineering, and design applications where circular elements need to be fitted around equilateral triangular shapes.

4. Using the Calculator

Tips: Enter the perimeter of the equilateral triangle in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between side length and circumradius?
A: For an equilateral triangle with side length 'a', the circumradius is \( r_c = \frac{a}{\sqrt{3}} \).

Q2: How is this formula derived from the side length formula?
A: Since perimeter P = 3a, we substitute a = P/3 into the side length formula \( r_c = \frac{a}{\sqrt{3}} \) to get \( r_c = \frac{P}{3\sqrt{3}} \).

Q3: What are the units for circumradius?
A: The circumradius has the same units as the perimeter input (typically meters or centimeters).

Q4: Can this calculator be used for other types of triangles?
A: No, this specific formula only applies to equilateral triangles where all sides and angles are equal.

Q5: What is the approximate value of the denominator?
A: \( 3\sqrt{3} \approx 5.196 \), so the circumradius is approximately P/5.196.