Triangle area formulas

1.
\begin{aligned} \text{Area of a triangle =} \frac{1}{2}*Base*Height \\
\text{Area of a triangle =}\sqrt{s(s-a)(s-b)(s-c)}, \\
\end{aligned}
where a, b, c are the sides of a triangle and
\begin{aligned}
s= \frac{1}{2}(a+b+c) \\
\end{aligned}

2. Area of equilateral Triangle = \begin{aligned}
\frac{\sqrt{3}}{4}*(side)^2
\end{aligned}

3. Radius of incircle of an equilateral triangle of side a = \begin{aligned}
\frac{a}{2\sqrt{3}}
\end{aligned}

4. Radius of circumcircle of an equilateral triangle of side a = \begin{aligned}
\frac{a}{\sqrt{3}}
\end{aligned}

5. Radius of incircle of a triangle of area a and semi-perimeter s = \begin{aligned}
\frac{a}{s}
\end{aligned}