1. What is the Inradius of Equilateral Triangle?

The Inradius of Equilateral Triangle is defined as the radius of the circle which is inscribed inside the triangle. For an equilateral triangle, the inradius can be calculated as one-third of the median length.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( Inradius \) - Radius of the inscribed circle (measured in meters)
• \( Median \) - Line segment joining a vertex to the midpoint of the opposite side (measured in meters)

Explanation: In an equilateral triangle, all medians are equal in length and the inradius is exactly one-third of the median length.

3. Importance of Inradius Calculation

Details: Calculating the inradius is important for various geometric applications, including determining the area of the inscribed circle and understanding the geometric properties of equilateral triangles.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is the inradius exactly one-third of the median in an equilateral triangle?
A: Due to the symmetry and equal properties of equilateral triangles, the centroid (where medians intersect) divides each median in a 2:1 ratio, making the inradius equal to one-third of the median length.

Q2: Are all medians equal in an equilateral triangle?
A: Yes, in an equilateral triangle, all medians are equal in length due to the symmetry of the triangle.

Q3: Can this formula be used for other types of triangles?
A: No, this specific relationship (inradius = 1/3 × median) only applies to equilateral triangles. Other triangle types have different relationships between inradius and medians.

Q4: What are some practical applications of calculating inradius?
A: Inradius calculations are used in engineering design, architecture, and various geometric problems involving inscribed circles within triangular shapes.

Q5: How does the inradius relate to other properties of equilateral triangles?
A: The inradius is also related to the side length (a) of the equilateral triangle by the formula: \( Inradius = \frac{a\sqrt{3}}{6} \).