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Triangles

Area of a Triangle


There are numerous ways to determine the area of a triangle. Each calculation method depends on what information is already known about the triangle in question.

Right Triangle
Right Triangle

Given the height and width of a right triangle, the area is simply:

\(A=\frac{1}{2}ab\)


Any Triangle
Any Triangle

Given the height and and base edge length of any triangle, the area is similarly:

\(A=\frac{1}{2}bh\)


Any Triangle
Any Triangle

Given one angle and is adjacent lengths, the area is:

\(A=\frac{1}{2}bc\,sin\,α\)


Any Triangle
Any Triangle

Given one side and its two adjacent angles, the area is:

\(A=\frac{a^2\,sin\,α\,sin\,β}{2\,sin(α+β)}\)


Any Triangle
Any Triangle

Given all three side lengths, we use Heron's formula (aka Hero's formula):

\(A=\sqrt{s(s-a)(s-b)(s-c)}\)

Where \(s\) is the semiperimeter:

\(s=\frac{1}{2}(a+b+c)\)


Inscribed Circle
Inscribed Circle

Note that a circle inscribed within any triangle has the property:

\(r=\frac{A}{s}\)








Geometry: Introduction Geometry: Regular Polygons