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. In an equilateral triangle, all sides are equal and all angles are 60 degrees.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the circumradius based on the semiperimeter of the equilateral triangle, utilizing the mathematical relationship between these geometric properties.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry and various engineering applications where circular patterns or circumscribed circles around equilateral triangles are involved.

4. Using the Calculator

Tips: Enter the semiperimeter value in meters. The value must be positive and valid.

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 semiperimeter related to side length?
A: Semiperimeter s = 3a/2, where a is the side length of the equilateral triangle.

Q3: Can this formula be used for other types of triangles?
A: No, this specific formula applies only to equilateral triangles. Other triangle types have different circumradius formulas.

Q4: What are practical applications of circumradius calculation?
A: Used in architecture, mechanical engineering, computer graphics, and any field involving geometric design and circular patterns.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles, though real-world measurements may introduce some error.