Parallelogram
A Quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equalsides is called a Rhombus, and a parallelogram whose Angles are all Right Angles is called a Rectangle.
A parallelogram of base 
and height 
has Area
 | (1) |
 | (2) |
 |  |  | (3) |
 | |  | (4) |
|  | (5) |
(Beyer 1987).
The Area of the parallelogram with sides formed by the Vectors 
and 
is
 | (6) |
with area 
and linear transformation 
, the Area of 
is | (7) |
As shown by Euclid, 
if lines parallel to the sides are drawn through any point on a diagonal of aparallelogram, then the parallelograms not containing segments of that diagonal are equal in Area (and conversely), soin the above figure, 
(Johnson 1929).
References
Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 123, 1987. Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 61, 1929.
- Energy
- En-Function
- Engel's Theorem
- Enneacontagon
- Enneacontahedron
- Enneadecagon
- Enneagon
- Enneagonal Number
- Enneakaidecagon
- Enneper's Minimal Surface
- Enneper's Negative Curvature Surfaces
- Enneper-Weierstraß Parameterization
- Enormous Theorem
- Enriques Surfaces
- Entire Function
- Entringer Number
- Entropy
- Entscheidungsproblem
- Enumerative Geometry
- Envelope
- Envelope Theorem
- Envyfree
- e-Perfect Number
- Epicycloid
- Epicycloid--1-Cusped