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Equal Areas

E is a midpoint of side GO, and D is a midpoint of side RO. Explain why triangle GOR has the same area as rectangle MATH.

View a Geometer's Sketchpad template or a Java construction of this sketch to convince yourself.


Examine one particular solution to this investigation (if you haven't already):

Construct segment ED. How does this segment compare with some of the other segments in the figure? Use this segment to explain why triangle GOR and rectangle MATH have the same area.

 Related External Resources

Heron's Area of a Triangle
This site will take you through some historical explorations, some interactive activities, and some intriguing connections in mathematics.

Geoboards in the Classroom
This unit deals with the side lengths and area of two-dimensional geometric figures using the geoboard as a pedagogical device.

Submit your idea for an investigation to InterMath.