Area of a triangle

There are several ways to compute the area of a triangle. The most common formula is $Area={\frac {1}{2}}bh$, where $b$ is the base, which can be any side, and $h$ is the altitude of the triangle, which is the perpendicular distance from the base (or the line containing the base for obtuse triangles) to the corner opposite the base. This formula does require that the altitude be known; other formulae not having this requirement are:

• $Area=\left({\frac {1}{2}}\right)bc(sinA)=\left({\frac {1}{2}}\right)ac(sinB)=\left({\frac {1}{2}}\right)ab(sinC)$
• $Area={\sqrt {s(s-a)(s-b)(s-c)}}$

where $s={\frac {1}{2}}(a+b+c)$is the semiperimeter of the triangle. This formula is known as the Heron's formula (or Hero's formula), named after the mathematician, Heron of Alexandria.

Triangle

Right triangles

For right triangles, the angle C, opposite the hypotenuse (c), is 90 degrees. The sine of 90 degrees is 1, so the equation reduces to:

$Area=\left({\frac {1}{2}}\right)ab$