geometry formulas for area and perimeter of shapes

Ellipse

circle area and perimeter formula
$$\textbf{Area of the ellipse}$$
$$A = \pi a b$$
$$\textbf{Perimeter of the ellipse}$$
$$4 a \int_{0}^{\frac{\pi}{2}}\sqrt{1- k^2 \sin^2(\theta)} d\theta ,$$
$$k = \frac{\sqrt{a^2-b^2}}{a}$$
$$\approx 2 \pi \sqrt{ (a^2+b^2})$$
$$$$