#### 4.9 Triangle Area

For determine the area of a triangle we can use several way.

we indicate $\overline{AD} = h$ the height of the triangle on side a:

$Area = \dfrac{1}{2}~( a h )$ $Area = \dfrac{1}{2} ~a~(b \sin{\gamma}) ~=~\dfrac{1}{2} ~a~(c \sin{\beta})$ $Area =\left( \dfrac{b^2}{2} \right)~ \dfrac{\sin{\alpha}\sin{\gamma}}{\sin{\beta}}$ $Area =\left( \dfrac{ab}{2} \right) ~2~ \sin{\dfrac{\gamma}{2}} \cos{\dfrac{\gamma}{2}}$

Consider semiperimeter: $p=\frac{1}{2} (a+b+c)$ we have:

$Area = ab \sqrt{\dfrac{(p-a)(p-b)}{ab}} \sqrt{\dfrac{p(p-c)}{ab}}$ $Area=\sqrt{p(p-a)(p-b)(p-c)}$