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The inradius of an equilateral triangle is the radius of the largest circle that fits inside the triangle, tangent to all three sides. For an equilateral triangle, this circle is called the incircle.
The calculator uses the formula:
Where:
Explanation: This formula derives from the relationship between the area of an equilateral triangle and its inradius, using the mathematical constant √3.
Details: Calculating the inradius is important in geometry for determining the size of the inscribed circle, which has applications in various fields including engineering, architecture, and design where circular elements need to fit within triangular spaces.
Tips: Enter the area of the equilateral triangle in square meters. The area must be a positive value greater than zero.
Q1: What is the relationship between inradius and side length?
A: For an equilateral triangle with side length s, the inradius is \( r_i = \frac{s\sqrt{3}}{6} \).
Q2: How is this formula derived?
A: The formula is derived from the standard area formula of an equilateral triangle \( A = \frac{\sqrt{3}}{4}s^2 \) and the inradius formula \( r_i = \frac{s\sqrt{3}}{6} \), then solving for rᵢ in terms of A.
Q3: Can this calculator be used for other types of triangles?
A: No, this specific formula only applies to equilateral triangles. Other triangle types have different formulas for calculating inradius.
Q4: What are practical applications of knowing the inradius?
A: Applications include designing circular components that fit within triangular frames, calculating material requirements, and solving geometric optimization problems.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect equilateral triangles. The accuracy depends on the precision of the input area value.