## The area of a triangle
Drag the angle slider to rotate a copy of the triangle 180° around the midpoint of a side.
These two triangles make a parallelogram with the same base and height as the original triangle.
When the angle reaches 180°, a new slider will appear. Drag this to 1.
This cuts the parallelogram into two congruent pieces, then slides one of them along the base to make a rectangle with the same base and height as the original triangle.
Conclusion: The area of a triangle is half the area of a rectangle with the same base and height.
To use this fact to find the area of a triangle
- Choose a base for the triangle (this applet shows a particular base, but you can use any side)
- Measure the length of the base and the height of the triangle, perpendicular to the base.
- Multiply to get the area of the rectangle.
- Take half of that to get the area of the triangle.
Formula:
Susan Addington, Created with GeoGebra |