Home
Back
Inradius of Equilateral Triangle Formula:
| From: | To: |
The Inradius of Equilateral Triangle is defined as the radius of the circle which is inscribed inside the triangle. It represents the distance from the center of the inscribed circle to any side of the equilateral triangle.
The calculator uses the formula:
Where:
Explanation: The formula calculates the inradius by dividing the perimeter by 6 times the square root of 3, which is derived from the geometric properties of equilateral triangles.
Details: Calculating the inradius is important in geometry and engineering applications where the largest possible circle that fits inside an equilateral triangle needs to be determined. It's also used in various design and construction calculations.
Tips: Enter the perimeter of the equilateral triangle in meters. The value must be positive and greater than zero. The calculator will compute the inradius using the mathematical formula.
Q1: What is the relationship between inradius and side length?
A: For an equilateral triangle with side length 'a', the inradius is \( \frac{a\sqrt{3}}{6} \), and since perimeter P = 3a, we get \( r_i = \frac{P}{6\sqrt{3}} \).
Q2: How does inradius relate to circumradius?
A: In an equilateral triangle, the inradius is exactly half of the circumradius.
Q3: 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 formulas for calculating inradius.
Q4: What are practical applications of inradius calculation?
A: Inradius calculations are used in engineering design, architecture, manufacturing (for fitting components), and various geometric problem-solving scenarios.
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 perimeter value.