## Equilateral Triangle Shape

A = angle A

a = side a

B = angle B

b = side b

C = angle C

c = side c

K = area

P = perimeter

s = semiperimeter

*h* = altitude

## Equilateral Triangle Calculator

An equilateral triangle is a special case of a triangle where all 3 sides have equal length and all 3 angles are equal to 60 degrees. The altitude shown *h* is *h*b or, the altitude of b. For equilateral triangles *h = h*a = *h*b = *h*c.

If you have any 1 known you can find the other 4 unknowns. So, if you know the length of a side = a, or the perimeter = P, or the semiperimeter = s, or the area = K, or the altitude = *h*, you can calculate the other values. Below are the 5 different choices of calculations you can make with this equilateral triangle calculator. Let us know if you have any other suggestions!

### Formulas and Calculations for a equilateral triangle:

- Perimeter of Equilateral Triangle: P = 3a
- Semiperimeter of Equilateral Triangle: s = 3a / 2
- Area of Equilateral Triangle: K = (1/4) * √3 * a
^{2}
- Altitude of Equilateral Triangle
*h* = (1/2) * √3 * a
- Angles of Equilateral Triangle: A = B = C = 60°
- Sides of Equilateral Triangle: a = b = c

### 1. Given the side find the perimeter, semiperimeter, area and altitude

- a is known; find P, s, K and
*h*
- P = 3a
- s = 3a / 2
- K = (1/4) * √3 * a
^{2}
*h* = (1/2) * √3 * a

### 2. Given the perimeter find the side, semiperimeter, area and altitude

- P is known; find a, s, K and
*h*
- a = P/3
- s = 3a / 2
- K = (1/4) * √3 * a
^{2}
*h* = (1/2) * √3 * a

### 3. Given the semiperimeter find the side, perimeter, area and altitude

- s is known; find a, P, K and
*h*
- a = 2s / 3
- P = 3a
- K = (1/4) * √3 * a
^{2}
*h* = (1/2) * √3 * a

### 4. Given the area find the side, perimeter, semiperimeter and altitude

- K is known; find a, P, s and
*h*
- a = √ [ (4 / √3) * K ] = 2 * √ [ K / √3 ]
- P = 3a
- s = 3a / 2
*h* = (1/2) * √3 * a

### 5. Given the altitude find the side, perimeter, semiperimeter and area

*h* is known; find a, P, s and K
- a = (2 / √3) * h
- P = 3a
- s = 3a / 2
- K = (1/4) * √3 * a
^{2}

For more information on triangles see:

Weisstein, Eric W. "Equilateral Triangle."
From *MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/EquilateralTriangle.html

Weisstein, Eric W. "Altitude." From *MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/Altitude.html