List of formulas in elementary geometry

Short description: none

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

## Contents

* 1 Two-dimensional shapes
* 2 Three-dimensional shapes
* 2.1 Sphere
* 3 See also
* 4 References

## Two-dimensional shapes

Shape | Area | Perimeter/Circumference | Meanings of symbols

|
|
|

Square | l2 | 4l | l is the length of a side
Rectangle | lb | 2(l+b) | l is length, b is breadth
Circle | πr2 | 2πr or πd | where r is the radius and d is the diameter
Ellipse | πab |  | where a is the semimajor axis and b is the semiminor axis
Triangle | bh2 | 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+b2h |  | a and b are the bases

Sources:[1][2][3]

## Three-dimensional shapes

Illustration of the shapes' equation terms

Cube

Cuboid

Prism

Parallelepiped

Pyramids

Tetrahedron

Cone

Cylinder

Sphere

Ellipsoid

This is a list of volume formulas of basic shapes:[4]: 405–406

* Cone – 13πr2h, where r is the base's radius and h is the cone's height;
* Cube – a3, where a is the side's length;
* Cuboid – abc, where a, b, and c are the sides' length;
* Cylinder – πr2h, where r is the base's radius and h is the cylinder's height;
* Ellipsoid – 43πabc, where a, b, and c are the semi-major and semi-minor axes' length;
* Sphere – 43πr3, where r is the radius;
* Parallelepiped – abcK, where a, b, and c are the sides' length,K=1+2cos⁡(α)cos⁡(β)cos⁡(γ)−cos2(α)−cos2(β)−cos2(γ), and α, β, and γ are angles between the two sides;
* Prism – Bh, where B is the base's area and h is the prism's height;
* Pyramid – 13Bh, where B is the base's area and h is the pyramid's height;
* Tetrahedron – 212a3, where a is the side's length.

### Sphere

See also: Volume of an n-ball and n-sphere § Volume and surface area

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=2πr is the circumference (the length of any one of its great circles),
* S is the surface area,
* V is the volume.

Surface area:

S=4πr2=1πC2=π(6V)23

Volume:

V=43πr3=16π2C3=16πS3/2

Radius:

r=12πC=14πS=34πV3

Circumference:

C=2πr=πS=π26V3

## See also

* Arc length - Distance along a curve
* Physics:List of second moments of area - None
* List of trigonometric identities

## References

1. ↑ "Archived copy". Archived from the original on 2012-08-13. https://web.archive.org/web/20120813015606/http://www.austincc.edu/tutor/students/resources/Geometry.pdf. Retrieved 2011-11-29.
2. ↑ "Area Formulas". http://www.math.com/tables/geometry/areas.htm.
3. ↑ "List of Basic Geometry Formulas". 27 May 2018. https://www.andlearning.org/geometry-formulas/.
4. ↑ Treese, Steven A. (2018). History and Measurement of the Base and Derived Units. Cham, Switzerland: Springer Science+Business Media. ISBN 978-3-319-77577-7. OCLC 1036766223.

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