List of formulas in elementary geometry

This is a short list of some common mathematical shapes and figures and the formulas that describe them.

Two-dimensional shapes

 * Sources:

Three-dimensional shapes
This is a list of volume formulas of basic shapes:


 * Cone – $\frac{1}{3}\pi r^2 h$, where $r$ is the base's radius
 * Cube – $a^3$, where $a$ is the side's length;
 * Cuboid – $abc$, where $a$ , $b$ , and $c$ are the sides' length;
 * Cylinder – $\pi r^2 h$, where $r$ is the base's radius and $h$  is the cone's height;
 * Ellipsoid – $\frac{4}{3}\pi abc$, where $a$ , $b$ , and $c$ are the semi-major and semi-minor axes' length;
 * Sphere – $\frac{4}{3}\pi r^3 $, where $r$ is the radius;
 * Parallelepiped – $abc\sqrt{K}$, where $a$ , $b$ , and $c$ are the sides' length,$K = 1 + 2\cos(\alpha)\cos(\beta)\cos(\gamma) - \cos^2(\alpha) - \cos^2(\beta) - \cos^2(\gamma)$ , and $\alpha$ , $\beta$ , and $\gamma$  are angles between the two sides;
 * Prism – $Bh$, where $B$ is the base's area and $h$  is the prism's height;
 * Pyramid – $\frac{1}{3}Bh$, where $B$ is the base's area and $h$  is the pyramid's height;
 * Tetrahedron – ${\sqrt{2}\over12}a^3$, where $a$ is the side's length.

Sphere
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables
 * $$r$$ is the radius,
 * $$C = 2 \pi r$$ is the circumference (the length of any one of its great circles),
 * $$S$$ is the surface area,
 * $$V$$ is the volume.

Surface area:

$$\begin{alignat}{4} S &= 4 \pi r^2 \\[0.3ex] &= \frac{1}{\pi} C^2 \\[0.3ex] &= \sqrt[3]{\pi (6 V)^2} \\[0.3ex] \end{alignat}$$

Volume:

$$\begin{alignat}{4} V &= \frac{4}{3} \pi r^3 \\[0.3ex] &= \frac{1}{6 \pi^2} C^3 \\[0.3ex] &= \frac{1}{6 \sqrt{\pi}} S^{3/2} \\[0.3ex] \end{alignat}$$

Radius:

$$\begin{alignat}{4} r &= \frac{1}{2 \pi} C \\[0.3ex] &= \sqrt{\frac{1}{4 \pi} S} \\[0.3ex] &= \sqrt[3]{\frac{3}{4 \pi} V} \\[0.3ex] \end{alignat}$$

Circumference:

$$\begin{alignat}{4} C &= 2 \pi r \\[0.3ex] &= \sqrt{\pi S} \\[0.3ex] &= \sqrt[3]{\pi^2 6 V} \\[0.3ex] \end{alignat}$$