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 = $$\begin{aligned} \frac{a}{s} \end{aligned}$$