Semiperimeter Of Equilateral Triangle Given Exradius Calculator

Formula Used:

\[ s = \sqrt{3} \times r_e \]

Semiperimeter of Equilateral Triangle (s):

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1. What is the Semiperimeter of Equilateral Triangle given Exradius?

The Semiperimeter of an Equilateral Triangle is half of the sum of the length of all sides of the triangle. When given the exradius (radius of the escribed circle), it can be calculated using the formula \( s = \sqrt{3} \times r_e \).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ s = \sqrt{3} \times r_e \]

Where:

\( s \) — Semiperimeter of Equilateral Triangle (m)
\( r_e \) — Exradius of Equilateral Triangle (m)
\( \sqrt{3} \) — Mathematical constant approximately equal to 1.732

Explanation: This formula establishes a direct relationship between the exradius and the semiperimeter of an equilateral triangle, utilizing the mathematical constant √3.

3. Importance of Semiperimeter Calculation

Details: The semiperimeter is a fundamental geometric property used in various triangle calculations, including area determination using Heron's formula and other geometric computations.

4. Using the Calculator

Tips: Enter the exradius value in meters. The value must be positive and valid (exradius > 0).

5. Frequently Asked Questions (FAQ)

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 the semiperimeter related to the perimeter?
A: The semiperimeter is exactly half of the perimeter of the triangle. For an equilateral triangle with side length a, both perimeter and semiperimeter can be expressed in terms of the exradius.

Q3: Can this formula be used for other types of triangles?
A: No, this specific formula \( s = \sqrt{3} \times r_e \) applies only to equilateral triangles due to their symmetrical properties.

Q4: What are the units of measurement?
A: Both semiperimeter and exradius are measured in meters (m), though any consistent unit of length can be used.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, as it's derived from the geometric properties of equilateral triangles. The accuracy depends on the precision of the input exradius value.