1. What is Exradius of Equilateral Triangle?

The Exradius of an Equilateral Triangle is the radius of the escribed circle (excircle) of the triangle. It is a circle tangent to one side of the triangle and 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)
• \( r_i \) — Inradius of Equilateral Triangle (m)

Explanation: In an equilateral triangle, the exradius is exactly three times the inradius. This relationship holds true for all equilateral triangles regardless of their size.

3. Formula Explanation

Details: The formula demonstrates the fixed ratio between the exradius and inradius in equilateral triangles. This mathematical relationship simplifies calculations involving these geometric properties.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and greater than zero. The calculator will compute the corresponding exradius.

5. Frequently Asked Questions (FAQ)

Q1: Why is the exradius exactly three times the inradius?
A: This is a unique property of equilateral triangles due to their perfect symmetry and equal side lengths.

Q2: Does this formula work for all types of triangles?
A: No, this specific relationship (re = 3 × ri) only applies to equilateral triangles. Other triangle types have different relationships between exradius and inradius.

Q3: What are typical units for these measurements?
A: Both inradius and exradius are typically measured in meters (m), but any consistent length unit can be used as long as both values use the same unit.

Q4: Can this formula be derived from triangle geometry?
A: Yes, the relationship can be derived using geometric properties of equilateral triangles and the formulas for calculating inradius and exradius.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles. The accuracy depends on the precision of the input value.