1. What is the Exradius of Equilateral Triangle?

The exradius of an equilateral triangle is the radius of the excircle (escribed circle) of the triangle. It is a circle lying outside the triangle, tangent to one of its sides 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)
• \( A \) — Area of Equilateral Triangle (m²)
• \( \sqrt{3} \) — Mathematical constant approximately equal to 1.732

Explanation: This formula calculates the exradius of an equilateral triangle based on its area, using the mathematical relationship between the area and the exradius.

3. Importance of Exradius Calculation

Details: Calculating the exradius is important in geometry and various engineering applications where the properties of circles tangent to triangles need to be determined.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between inradius and exradius?
A: The inradius is the radius of the inscribed circle (inside the triangle), while the exradius is the radius of the excircle (outside the triangle).

Q2: Can this formula be used for any triangle?
A: No, this specific formula is only valid for equilateral triangles. Other triangle types have different formulas for calculating exradius.

Q3: How is the exradius related to the side length?
A: For an equilateral triangle with side length 'a', the exradius can also be calculated as \( r_e = \frac{a\sqrt{3}}{2} \).

Q4: What are practical applications of exradius calculation?
A: Exradius calculations are used in various fields including architecture, mechanical engineering, and computer graphics where geometric properties need to be determined.

Q5: Is the exradius always larger than the inradius?
A: Yes, for an equilateral triangle, the exradius is always larger than the inradius.