October 15th, 2021

High School Resource: Area vs. Perimeter of a Triangle by Math Open Reference

High School Resource

Area vs. Perimeter of a Triangle by Math Open Reference

This interactive web-based resource shows the relationship between the perimeter and area of a triangle. It shows that a triangle with a constant perimeter does not have a constant area.

The user is given a triangle with one changeable vertex and a constant perimeter. As you drag the vertex, it is clear that the area changes, even though the perimeter remains constant. The user is also provided the option of viewing the path traced by the dragged vertex and see that it forms an ellipse. A link is provided to take the user to a page where this effect is exploited to construct an ellipse with string and pins.

This web page can be enlarged to full screen size for use with a classroom projector. After use in the classroom, students can access it again from any web browser at home or in the library with no login required.

Related NY State Academic Standards: G-C.5, G-GMD.1, and MST3.A1.G.1!

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