Area of a triangle

While we do have a couple of calculators for finding the area of a triangle (see Area of triangle by coordinates and Heron's formula calculator), there are other methods, depending on what you know about the triangle. Here is the universal calculator where you can choose the formula to calculate a triangle area.

The following formulas are supported:

• Half of base times height formula - if you know the base and the altitude of a triangle
• Heron's formula - if you know all three sides of a triangle
• Side-angle-side formula - if you know two sides and included angle
• Coordinates formula - if you know the coordinates of the three vertices of a triangle
• Equilateral triangle formula - formula for the equilateral triangle, which is simplified Heron's formula

You can find all formulas with descriptions below the calculator.

Area of a triangle

Find the area fromthe base and the height the lengths of all sides two sides and included angle coordinates of the vertexes side length of the equilateral triangle

Base length

Height length

Side length

Side length

Side length

Sine

°

′

″

First vertex x

First vertex y

Second vertex x

Second vertex y

Third vertex x

Third vertex y

Side length

Calculate

Calculation precision

Digits after the decimal point: 2

Half of base times height formula

Heron's formula

Side angle side formula

Coordinates formula

Equilateral triangle formula

 

Area of the triangle

 

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Half of base times height formula

You can find the triangle area from the length of the base and the length of the corresponding altitude. Any side can be the base, but the altitude must correspond to the base. The formula is

where A is the area, a is the length of the base, h is the altitude's length.

Heron's formula

You can find the area of a triangle if you know the lengths of all sides. The formula is

where A is the area, a, b, c are the lengths of the sides, p is the perimeter divided by 2 (semi-perimeter) .

The formula is named after Hero of Alexandria, a Greek Engineer and Mathematician, in 10 - 70 AD. A proof can be found in his book Metrica written around 60 AD.

Side-angle-side formula

Also referred to as SAS, this formula allows you to find a triangle area if you know two sides and the angle at a common vertex (included angle). The formula is

where A is the area, a and b are the sides' lengths, alpha is the angle at the common vertex.

Actually, this form directly follows from half of the base times height formula because the triangle's height would be .

Coordinates formula

Using this formula, you can find a triangle area if you know the cartesian coordinates of all three vertexes of a triangle. If the vertexes have coordinates like (x1, y1), (x2, y2) and (x3, y3) then the formula is

where A is the area, and x and y are coordinates of triangle vertexes.

Well, you can also compute the cartesian distance between the vertexes and use Heron's formula.

Equilateral triangle formula

This is just simplified Heron's formula because all sides are equal. The formula is

where A is the area, a is the length of the side.