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# Equilateral triangle

This online calculator calculates characteristics of the equilateral triangle: the length of the sides, the area, the perimeter, the radius of the circumscribed circle, the radius of the inscribed circle, the altitude (height) from single known value

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle.

In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors, and the medians to each side coincide.1

Because of the regular nature of the equilateral triangle, we can determine many of its quantities from a single known value. That is, if you know either the length of the sides, the area of the equilateral triangle, the perimeter of the triangle, the radius of the circumscribed circle, the radius of the inscribed circle or the altitude (height) of the triangle, you can find all other quantities.

Use this calculator before to input known value and compute all other values. The related formulas are listed under the calculator for reference.

#### Equilateral triangle

Digits after the decimal point: 2
The length of the sides

The area

The perimeter

The radius of the circumscribed circle

The radius of the inscribed circle

The altitude (height)

## Equilateral triangle formulas

Let a be the length of the sides, A - the area of the triangle, p the perimeter, R - the radius of the circumscribed circle, r - the radius of the inscribed circle, h - the altitude (height) from any side.

These values are connected by these formulas below:

$A=\frac{\sqrt{3}}{4}a^2 \\ \\ p=3a \\ \\ R=\frac{a}{\sqrt{3}} \\ \\ r = \frac{\sqrt{3}}{6}a \\ \\ h = \frac{\sqrt{3}}{2}a$

There are some shortcut formulas where you can find values directly from the altitude (height) of the triangle if you know it without first computing the length of the side.

$A=\frac{h^2}{\sqrt{3}} \\ \\ R = \frac{2h}{3} \\ \\ r=\frac{h}{3}$.

By the way, note that the apothem, or the height of the center from each side also is $\frac{h}{3}$

PLANETCALC, Equilateral triangle