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# Area of an Equilateral Triangle Definition

The area of an equilateral triangle is calculated using the formula: A = s2 3 4 where s represents the equilateral triangles common side length.

Conversely to solve for the common side length of an equilateral triangle given the area you can rearrange the equation to get: s =  4A 3   where A represents the area of the equilateral triangle.

The diagram below illustrates an equilateral triangle and its associated angle formula.

## Properties

Denoting the common length of the sides of the equilateral triangle as s, we can determine using the Pythagorean theorem that:

• The area: A = s2 3 4

• The perimeter: p = 3s.

• The radius of the circumscribed circle: R =

• The radius of the inscribed circle: r = or r =

• The geometric center of the triangle is the center of the circumscribed and inscribed circles.

• The altitude (height) from any side is h =

• Denoting the radius of the circumscribed circle as R, we can determine using trigonometry that:

• The area of the triangle is: A =

• Many of these quantities have simple relationships to the altitude (h) of each vertex from the opposite side:

• The area is: A =

• The height of the center from each side or apothem is:

• The radius of the circle circumscribing the three vertices is: R =

• The radius of the inscribed circle is: r =

• In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors, and the medians to each side coincide.

### Sources

Equilateral Triangle. 18 Sept. 2020, en.wikipedia.org/wiki/Equilateral_triangle.

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