The area of a triangle 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 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

Quadrivium

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