geometry formulas for area and perimeter of shapes

Parabola

circle area and perimeter formula
$$\textbf{Area of the parabola}$$
$$A = \frac{2}{3} a b$$
$$\textbf{Length,}\textit{ ABC}$$
$$\vert ABC \vert = \sqrt{b^2+16 a^2}+$$
$$\frac{b^2}{8 a} \ln{\Bigg(\frac{4 a + \sqrt{b^2+16 a^2}}{b}}\Bigg)$$