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The area of an equilateral triangle can be calculated using its circumradius. The circumradius is the radius of the circle that passes through all three vertices of the triangle. This formula provides a direct relationship between the circumradius and the area of an equilateral triangle.
The calculator uses the formula:
Where:
Explanation: The formula calculates the area of an equilateral triangle by squaring the circumradius and multiplying it by the constant factor \( \frac{3\sqrt{3}}{4} \).
Details: Calculating the area of an equilateral triangle using circumradius is useful in geometry problems, engineering applications, and architectural design where the circumradius might be known or easier to measure than side lengths.
Tips: Enter the circumradius value in meters. The value must be positive and greater than zero. The calculator will compute the area in square meters.
Q1: What is the relationship between circumradius and side length?
A: For an equilateral triangle, the side length \( a = \sqrt{3} \times r_c \), where \( r_c \) is the circumradius.
Q2: Can this formula be used for other types of triangles?
A: No, this specific formula only applies to equilateral triangles. Other triangle types have different relationships between circumradius and area.
Q3: What are typical units for circumradius and area?
A: Circumradius is typically measured in meters (m), and area in square meters (m²), though any consistent unit system can be used.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles. Real-world measurements may introduce some error.
Q5: Can I calculate circumradius from area using this formula?
A: Yes, the formula can be rearranged as \( r_c = \sqrt{\frac{4A}{3\sqrt{3}}} \) to find circumradius from area.