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Triangle Inside a Rectangle

A triangle has two shared vertices and one shared side with a rectangle. The third vertex is anywhere on the side opposite of the shared side (see figures above).

How does the area of the triangle compare with the area of the rectangle? Why do you think this relationship holds?

 Extensions

Where would you move the third vertex of the triangle to have a minimum perimeter? Explain why this position results in a minimum perimeter.

 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.

Animated area of a triangle [ Geometer's Sketchpad File ]
This page will show you how animation can be used to find the area of any triangle when the base and height of the triangles are the same.

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