Formulas for the Area of a Triangle

1. A = \frac{1}{2}b \cdot h, where b is the base and h is the altitude of the triangle.

2. The area of an equilateral triangle

A = \frac{{\sqrt 3 }}{4}{a^2}

, where a is the length of each side of the triangle.

3. The area of a triangle when two adjacent sides and the included angle is given by

\Delta = \frac{1}{2}a \cdot b\sin \theta

4. The area of a triangle when the length of all sides are given

\Delta = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)}


s = \frac{{a + b + c}}{2}

5. The area of a triangle with vertices A\left( {{x_1},{y_1}} \right),\,B\left( {{x_2},{y_2}} \right),\,C\left( {{x_3},{y_3}} \right) is given by the formulas

A = \frac{1}{2}\left| {\begin{array}{*{20}{c}} {{x_1}}&{{y_1}}&1 \\ {{x_2}}&{{y_2}}&1 \\ {{x_3}}&{{y_3}}&1 \end{array}} \right|