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The formula calculates the area of an equilateral triangle when the exradius (radius of the escribed circle) is known. It provides a direct relationship between the exradius and the area of the triangle.
The calculator uses the formula:
Where:
Explanation: The formula derives from the geometric relationship between the exradius and the side length of an equilateral triangle, and subsequently the area.
Details: Calculating the area of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. For equilateral triangles, this specific formula provides a quick way to determine area when the exradius is known.
Tips: Enter the exradius value in meters. The value must be positive and valid. The calculator will compute the area in square meters.
Q1: What is an exradius in an equilateral triangle?
A: The exradius is the radius of an escribed circle (excircle) of the triangle, which is a circle tangent to one side of the triangle and the extensions of the other two sides.
Q2: How is this formula derived?
A: The formula is derived from the relationship between the exradius and the side length of an equilateral triangle, combined with the standard area formula for an equilateral triangle.
Q3: Can this formula be used for all triangles?
A: No, this specific formula applies only to equilateral triangles where all sides and angles are equal.
Q4: What are the units for the result?
A: The area result is in square meters (m²) if the exradius input is in meters. The units will match the square of the input units.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input value. The precision depends on the accuracy of the input exradius measurement.