Area of Equilateral Triangle given Inradius Calculator

Area of Equilateral Triangle Formula:

\[ A = 3 \times \sqrt{3} \times r_i^2 \]

Area of Equilateral Triangle:

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1. What is the Area of Equilateral Triangle given Inradius?

The Area of an Equilateral Triangle given its Inradius is calculated using the formula that relates the area to the radius of the inscribed circle. This provides a direct way to determine the area when the inradius is known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = 3 \times \sqrt{3} \times r_i^2 \]

Where:

\( A \) — Area of Equilateral Triangle (m²)
\( r_i \) — Inradius of Equilateral Triangle (m)
\( \sqrt{3} \) — Square root of 3 (approximately 1.732)

Explanation: The formula demonstrates that the area of an equilateral triangle is proportional to the square of its inradius, scaled by the constant \( 3\sqrt{3} \).

3. Importance of Area Calculation

Details: Calculating the area of an equilateral triangle is fundamental in geometry and has applications in various fields including architecture, engineering, and design where triangular shapes are used.

4. Using the Calculator

Tips: Enter the inradius value in meters. The value must be positive and valid. The calculator will compute the area based on the mathematical relationship.

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: What is the inradius of a triangle?
A: The inradius is the radius of the largest circle that fits inside the triangle and is tangent to all three sides.

Q3: How is this formula derived?
A: The formula is derived from the relationship between the area, semiperimeter, and inradius of a triangle (A = r × s), combined with the specific properties of equilateral triangles.

Q4: 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 area formulas.

Q5: What are the units of measurement?
A: The inradius should be in meters (m) and the resulting area will be in square meters (m²). Consistent units must be used throughout the calculation.