**Dividing
triangles**

Find as many ways as you can to divide an arbitrary triangle into four equal-area
triangles. (Scher, Daniel, "A Triangle Divided: Investigating Equal Areas,"
*Mathematics Teaching* 93, 7, 10/00, p. 608. Problem taken from *Connected
Geometry* (EDC 2000))

**Approaches**

Quarter any side and join quartiles to opposite vertex (3 ways for 3 sides)

Draw any of the three medians, then subdivide the halves into halves (up to 27 ways).

Ignoring a quarter, subdivide the rest into three pieces.

Turn into equivalent rectangle, partition the rectangle, and rearrange pieces into the original triangle.

**Your
experience**

Have you used this problem with a class and seen approaches other than(or more specific than) those mentioned above? Or do you have other comments or criticisms or stories? If so, please tell us!

*Last updated 30 November, 2004*