The area of a trapezoid Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

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

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