1. What Is The Apothem Of An Equilateral Triangle?

The apothem of an equilateral triangle is the distance from the center of the triangle to the midpoint of any side. It represents the radius of the inscribed circle (incircle) and is perpendicular to the side it touches.

2. How Does The Calculator Work?

The calculator uses the apothem formula:

Where:

• \( a \) — Apothem length
• \( s \) — Side length of the equilateral triangle
• \( \tan(60^\circ) \) — Tangent of 60 degrees (approximately 1.732)

Explanation: The formula derives from the geometric properties of equilateral triangles where all angles are 60 degrees and all sides are equal.

3. Importance Of Apothem Calculation

Details: Calculating the apothem is essential for determining the area of regular polygons, finding the radius of inscribed circles, and solving various geometric problems involving equilateral triangles.

4. Using The Calculator

Tips: Enter the side length of the equilateral triangle in any consistent units. The result will be in the same units. The value must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between apothem and side length?
A: In an equilateral triangle, the apothem is exactly one-third of the height of the triangle.

Q2: Can this formula be used for other regular polygons?
A: No, this specific formula applies only to equilateral triangles. Other regular polygons have different apothem formulas.

Q3: How is the apothem related to the area of the triangle?
A: The area can be calculated as (perimeter × apothem)/2, which simplifies to (3s × a)/2 for an equilateral triangle.

Q4: What is the approximate value of the apothem for a unit equilateral triangle?
A: For a triangle with side length 1, the apothem is approximately 0.288675 units.

Q5: How does the apothem compare to the circumradius?
A: In an equilateral triangle, the apothem is exactly half the length of the circumradius (radius of the circumscribed circle).