1. What is the Exradius of Equilateral Triangle?

The Exradius of an Equilateral Triangle is the radius of the escribed circle (excircle) of the triangle. It is tangent to one side of the triangle and to the extensions of the other two sides.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula relates the exradius of an equilateral triangle to its semiperimeter through a simple mathematical relationship.

3. Importance of Exradius Calculation

Details: Calculating the exradius is important in geometry for understanding the properties of equilateral triangles and their associated circles, particularly in construction and design applications.

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 exradius and inradius?
A: In an equilateral triangle, the exradius is exactly twice the inradius.

Q2: 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 exradius formulas.

Q3: How is the semiperimeter related to the side length?
A: For an equilateral triangle with side length a, the semiperimeter s = 3a/2.

Q4: What are practical applications of exradius calculation?
A: Exradius calculations are used in engineering, architecture, and design where precise geometric relationships are important.

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