# 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

Shape Area Perimeter/Circumference
Square (where ${\displaystyle s}$ is the length of a side) ${\displaystyle A=s^{2}}$ ${\displaystyle P=4s}$
Rectangle ( ${\displaystyle l}$ is length, ${\displaystyle w}$ is width) ${\displaystyle A=lw}$ ${\displaystyle P=2l+2w}$
Circle (where ${\displaystyle r}$ is the radius and ${\displaystyle d}$ is the diameter) ${\displaystyle A=\pi r^{2}}$ ${\displaystyle C=2\pi r}$ or ${\displaystyle C=\pi d}$
Ellipse (where ${\displaystyle a}$ is the semimajor axis and ${\displaystyle b}$ is the semiminor axis) ${\displaystyle A=\pi ab}$
Triangle (${\displaystyle b}$ is base; ${\displaystyle h}$ is height; ${\displaystyle a,b,c}$ are sides) ${\displaystyle A={\frac {bh}{2}}}$ ${\displaystyle P=a+b+c}$
Parallelogram (${\displaystyle b}$ is base, ${\displaystyle h}$ is height, ${\displaystyle a}$ is side) ${\displaystyle A=bh}$ ${\displaystyle P=2a+2b}$
Trapezoid (where ${\displaystyle a}$ and ${\displaystyle b}$ are the bases) ${\displaystyle A={\frac {a+b}{2}}h}$
Sources:[1][2]

## Three-dimensional shapes

Shape Volume Surface area
Cube (where ${\displaystyle s}$ is the length of a side) ${\displaystyle V=s^{3}}$ ${\displaystyle 6s^{2}}$
Rectangular Prism (${\displaystyle l}$ = length, ${\displaystyle h}$ = height, ${\displaystyle w}$ = width) ${\displaystyle V=lwh}$ ${\displaystyle S=2lw+2lh+2wh}$
Sphere (where ${\displaystyle r}$ is the radius) ${\displaystyle V={\frac {4\pi r^{3}}{3}}}$ ${\displaystyle S=4\pi r^{2}}$
Right circular cylinder (where ${\displaystyle r}$ is the radius and ${\displaystyle h}$ is the height) ${\displaystyle V=\pi r^{2}h}$ ${\displaystyle S=2\pi rh+2\pi r^{2}}$
Sources:[3]