# 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]

[3]

## 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:[4]

## References

1. ^ "Archived copy" (PDF). Archived from the original (PDF) on 2012-08-13. Retrieved 2011-11-29.CS1 maint: archived copy as title (link)
2. ^ http://www.math.com/tables/geometry/areas.htm
3. ^ https://www.andlearning.org/geometry-formulas/
4. ^ http://www.math.com/tables/geometry/volumes.htm