1. What is Exradius of Equilateral Triangle?

The exradius of an equilateral triangle is the radius of the escribed circle (excircle) of the triangle. An excircle 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)
• \( h \) — Height of Equilateral Triangle (m)

Explanation: For an equilateral triangle, the exradius is equal to the height of the triangle.

3. Importance of Exradius Calculation

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

4. Using the Calculator

Tips: Enter the height of the equilateral triangle in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between exradius and height in an equilateral triangle?
A: In an equilateral triangle, the exradius is equal to the height of the triangle.

Q2: How is the exradius different from the inradius?
A: The exradius is the radius of the excircle (outside the triangle), while the inradius is the radius of the incircle (inside the triangle).

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

Q4: What are the practical applications of knowing the exradius?
A: Exradius calculations are used in geometric design, construction, and in various mathematical proofs and applications.

Q5: How does the exradius relate to the side length of an equilateral triangle?
A: For an equilateral triangle with side length a, the exradius can also be expressed as \( r_e = \frac{a\sqrt{3}}{2} \), which is equivalent to the height.