1. What is the Perimeter of Equilateral Triangle given Height Formula?

The formula calculates the perimeter of an equilateral triangle when the height is known. It is derived from the geometric properties of equilateral triangles and the Pythagorean theorem.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( P \) — Perimeter of Equilateral Triangle (m)
• \( h \) — Height of Equilateral Triangle (m)
• \( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: This formula is derived from the relationship between the height and side length of an equilateral triangle, where height = (√3/2) × side, and perimeter = 3 × side.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of an equilateral triangle is essential in various geometric applications, construction projects, and mathematical problem-solving where the height is known but the side length needs to be determined.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Why is there a square root of 3 in the formula?
A: The square root of 3 appears due to the geometric relationship between the height and side length in an equilateral triangle, derived from the Pythagorean theorem.

Q2: Can this formula be used for any triangle?
A: No, this specific formula applies only to equilateral triangles where all sides are equal and all angles are 60 degrees.

Q3: What are the units of measurement?
A: The calculator uses meters for both height and perimeter, but the formula works with any consistent unit of length.

Q4: How accurate is the calculation?
A: The calculation is mathematically exact, though the displayed result is rounded to 6 decimal places for practical purposes.

Q5: Can I calculate the side length from the perimeter?
A: Yes, for an equilateral triangle, side length = perimeter ÷ 3.