Area of a triangle

There are several ways to compute the area of a triangle.

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

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:

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