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The formula calculates the area of an equilateral triangle when its perimeter is known. An equilateral triangle has all three sides equal and all three angles equal to 60 degrees.
The calculator uses the formula:
Where:
Explanation: Since all sides are equal in an equilateral triangle, each side equals P/3. The area formula using side length is (√3/4) × side². Substituting P/3 for side gives us the perimeter-based formula.
Details: Calculating the area of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. For equilateral triangles, this calculation is particularly useful when the perimeter is known but individual side measurements aren't readily available.
Tips: Enter the perimeter of the equilateral triangle in meters. The value must be positive and greater than zero. The calculator will compute the area in square meters.
Q1: Why is there a √3 in the formula?
A: The √3 comes from the trigonometric relationships in an equilateral triangle, specifically from the height calculation which is (side × √3)/2.
Q2: Can this formula be used for any triangle?
A: No, this formula is specific to equilateral triangles where all sides are equal. For other triangles, different area formulas must be used.
Q3: What units should I use for the perimeter?
A: Use consistent units (meters, centimeters, inches, etc.). The area will be in square units of whatever unit you used for the perimeter.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact. Any inaccuracy would come from measurement error in the perimeter or rounding in the square root calculation.
Q5: What if I know the side length instead of perimeter?
A: If you know the side length (s), you can use the simpler formula: Area = (√3/4) × s², or multiply the side length by 3 to get the perimeter first.