Unizor - Geometry2D - Area - Basics
Channel: Zor Shekhtman on UNIZOR Education
Date: 2012-10-02

Proof of this is based on two statements that were explained in details in the Introduction:
(1) the areas of congruent geometric objects on a plane are equal;
(2) the area of a rectangle is equal to a product of lengths of any of its two sides

Parallelogram
Area of a parallelogram is equal to a product of the length of its one side by a length of an altitude drawn towards this side from one of two vertices not lying on this side.
 with a common vertex (traditionally called "width" and "height").

Triangle
Area of a triangle is equal to half of a product of the length of its one side by a length of an altitude drawn towards this side from an opposite vertex.

Trapezoid
Area of a trapezoid is equal to a product of the average length of its parallel bases (i.e. half the sum of their lengths) by a length of an altitude perpendicular to these bases.