List of formulas in elementary geometry explained

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

Two-dimensional shapes

Shape		Perimeter/Circumference	Meanings of symbols
Square	l ^{2}	4 l	l is the length of a side
Rectangle	lb	2 (l + b)	l is length, b is breadth
Circle	\pi r ^{2}	2 \pi r or \pi d	where r is the radius and d is the diameter
Ellipse	\pi ab		where a is the semimajor axis and b is the semiminor axis
Triangle	(bh)/(2)	a + b + c	b is base; h is height; a,b,c are sides
Parallelogram	bh	2 (a + b)	b is base, h is height, a is side
Trapezoid	(a + b)/(2) h		a and b are the bases

Sources:^{[1] [2] [3]}

Three-dimensional shapes

This is a list of volume formulas of basic shapes:^[4]

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

Sphere

See also: Volume of an n-ball.

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:

Volume:

Radius:

Circumference

Notes and References

1. Web site: Archived copy . 2011-11-29 . dead . https://web.archive.org/web/20120813015606/http://www.austincc.edu/tutor/students/resources/Geometry.pdf . 2012-08-13 .
2. Web site: Area Formulas.
3. Web site: List of Basic Geometry Formulas. 27 May 2018.
4. Book: Treese, Steven A. . History and Measurement of the Base and Derived Units . 2018 . . 978-3-319-77577-7 . Cham, Switzerland . 2018940415 . 1036766223.