1. What is the Median of Equilateral Triangle?

The Median of Equilateral Triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. In an equilateral triangle, all three medians are equal in length and intersect at the centroid.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( M \) — Median of Equilateral Triangle (m)
• \( r_e \) — Exradius of Equilateral Triangle (m)

Explanation: This formula establishes the direct relationship between the median and the exradius in an equilateral triangle, where the median equals the exradius.

3. Importance of Median Calculation

Details: Calculating the median is important in geometry for determining various properties of equilateral triangles, including centroid location, area division, and symmetry analysis.

4. Using the Calculator

Tips: Enter the exradius value in meters. The value must be positive and valid (exradius > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is an exradius in an equilateral triangle?
A: The exradius is the radius of an excircle tangent to one side of the triangle and the extensions of the other two sides.

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

Q3: How is the median related to other triangle elements?
A: In an equilateral triangle, the median is equal to the altitude, angle bisector, and perpendicular bisector.

Q4: What units should be used for input?
A: The calculator uses meters as the default unit, but any consistent unit of length can be used as long as it's consistent throughout.

Q5: Can this formula be used for non-equilateral triangles?
A: No, this specific formula only applies to equilateral triangles where all sides and angles are equal.