A Quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides 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) |

(7) |

As shown by Euclid, if lines parallel to the sides are drawn through any point on a diagonal of a parallelogram, then the parallelograms not containing segments of that diagonal are equal in Area (and conversely), so in 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.

© 1996-9

1999-05-26