1. What is the Inradius of Equilateral Triangle?

The Inradius of an Equilateral Triangle is defined as the radius of the circle which is inscribed inside the triangle. It is the distance from the center of the inscribed circle (incircle) to any side of the triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_i \) — Inradius of Equilateral Triangle (m)
• \( s \) — Semiperimeter of Equilateral Triangle (m)

Explanation: The formula calculates the radius of the inscribed circle based on the semiperimeter of the equilateral triangle, utilizing the mathematical constant √3.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important in geometry for determining the size of the largest circle that can fit inside an equilateral triangle, which has applications in various engineering and design fields.

4. Using the Calculator

Tips: Enter the semiperimeter 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 inradius and side length?
A: For an equilateral triangle with side length a, the inradius can also be calculated as \( r_i = \frac{a\sqrt{3}}{6} \).

Q2: How is semiperimeter related to side length?
A: For an equilateral triangle, semiperimeter \( s = \frac{3a}{2} \), where a is the side length.

Q3: 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 inradius formulas.

Q4: What are practical applications of inradius calculation?
A: Inradius calculations are used in manufacturing, architecture, and design where circular components need to fit within triangular spaces.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles, providing precise results based on the input values.