## The area of a trapezoid
Drag the angle slider to rotate a copy of the trapezoid 180° around the midpoint of a side.
These two trapezoids make a parallelogram whose base is the sum of the bases of the trapezoid, and with the same height as the original trapezoid.
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 whose base is the sum of the bases of the trapezoid, and with the same height as the original trapezoid.
**Conclusion: **The area of a trapezoid is half the area of a rectangle whose base is the sum of the bases of the trapezoid, and with the same height as the original trapezoid.
To use this fact to find the area of a trapezoid:
- Measure the two bases and add. Measure the height of the trapezoid, perpendicular to both bases.
- Multiply to get the area of the rectangle.
- Take half of that to get the area of the trapezoid.
Formula:
Susan Addington, Created with GeoGebra |