1. What is Exradius of Equilateral Triangle?

The Exradius of an Equilateral Triangle is the radius of the escribed circle (excircle) that is tangent to one side of the triangle and the extensions of the other two sides. In an equilateral triangle, all three exradii are equal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the exradius of an equilateral triangle based on its perimeter, utilizing the mathematical constant √3.

3. Importance of Exradius Calculation

Details: Calculating the exradius is important in geometry for understanding the properties of equilateral triangles and their relationship with circumscribed circles. It has applications in various fields including architecture, engineering, and computer graphics.

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

Q2: How is exradius related to side length?
A: For an equilateral triangle with side length a, the exradius is \( \frac{a\sqrt{3}}{2} \).

Q3: Are all three exradii equal in an equilateral triangle?
A: Yes, in an equilateral triangle, all three exradii are equal due to the symmetry of the triangle.

Q4: What is the difference between circumradius and exradius?
A: Circumradius is the radius of the circle passing through all three vertices, while exradius is the radius of a circle tangent to one side and the extensions of the other two sides.

Q5: 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 formulas for calculating exradius.