1. What is the Height of Equilateral Triangle?

The height of an equilateral triangle is the perpendicular distance from any vertex to the opposite side. In an equilateral triangle, all three sides are equal and all three angles are 60 degrees.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of the equilateral triangle
• \( P \) — Perimeter of the equilateral triangle
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

3. Formula Explanation

Details: The formula is derived from the relationship between the side length and height of an equilateral triangle. Since all sides are equal, the perimeter is 3 times the side length. The height can be found using the Pythagorean theorem in the right triangle formed by the height.

4. Using the Calculator

Tips: Enter the perimeter of the equilateral triangle in meters. The value must be greater than zero. The calculator will compute the height based on the mathematical formula.

5. Frequently Asked Questions (FAQ)

Q1: What is an equilateral triangle?
A: An equilateral triangle is a triangle with all three sides of equal length and all three angles equal to 60 degrees.

Q2: Why is the formula h = P/(2√3)?
A: This formula is derived from the relationship P = 3a (where a is side length) and h = (a√3)/2. Substituting gives h = P/(2√3).

Q3: What units should I use?
A: Use consistent units (meters, centimeters, etc.). The result will be in the same units as the input.

Q4: Can this calculator be used for other types of triangles?
A: No, this formula is specific to equilateral triangles where all sides are equal.

Q5: What if I know the side length instead of perimeter?
A: If you know the side length (a), the height can be calculated as h = (a√3)/2.