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 medians are equal in length and coincide with the altitudes and angle bisectors.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( M \) — Median of Equilateral Triangle (m)
• \( s \) — Semiperimeter of Equilateral Triangle (m)

Explanation: The formula calculates the median length using the semiperimeter of the equilateral triangle and the mathematical constant √3.

3. Importance of Median Calculation

Details: Calculating the median of an equilateral triangle is important in geometry for determining various properties of the triangle, including its center of mass and symmetry properties.

4. Using the Calculator

Tips: Enter the semiperimeter value in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between median and side length?
A: In an equilateral triangle, the median length is equal to \( \frac{\sqrt{3}}{2} \times \) side length.

Q2: Are all medians equal in an equilateral triangle?
A: Yes, in an equilateral triangle, all three medians are equal in length.

Q3: How is semiperimeter related to side length?
A: For an equilateral triangle, semiperimeter \( s = \frac{3a}{2} \), where a is the side length.

Q4: 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 median formulas.

Q5: What are the practical applications of median calculation?
A: Median calculations are used in engineering, architecture, and computer graphics for geometric modeling and analysis.