Descriptive Geometry/Mathematical Constructions/Area of a Triangle

The area of any right triangle is equal to the summation of the lengths of its sides. Therefore, any right triangle can be unfolded into a straight line whose length equals the triangle's area. By extension, any given triangle can have its area calculated in the same way as long as it is first converted to a right triangle.

To convert a triangle to a right triangle:

1) Choose one side to rotate until it is either vertical or horizontal, and rotate it until it's orthogonal.

2) Draw a line parallel to the now-orthogonal side of the triangle. Make sure it touches the point opposite the orthogonal side.

3) Move the point along the line until a right angle is formed.

4) Rotate the sides of the triangle to form a straight line. This line's length is equal to the area of the starting triangle.



http://mathworld.wolfram.com/RightTriangle.html

http://forumgeom.fau.edu/FG2006volume6/FG200639.pdf