RectTri Area vs. Perimeter Drafts

Scott Farrar, Jan 25, 2016

Drafts of an activity that allows students to explore the relationship between Areas and Perimeters in polygons. Focus is on triangles and rectangles. Possible extensions to other polygons and to the parabolas of Area as a function of a polygon's perimeter.

Table of Contents

  1. Introductory Possibilities
    1. The Rects of Integer Equilateral Triangles
    2. The Rects of a Triangle's Perimeter (positive reals)
    3. Rect-Tri-Areas
    4. Overflowing Rectangles
  2. "Act 2" providing tools for exploration
    1. Area v. Perim for Quads and Tris
    2. 2 Rects 2 Furious
  3. Views of "the solution"
    1. Answer to Equal Perim and Area Triangle,Rectangle
    2. Answer 2 to Equal Area, Perim of Rectangle, Triangle
    3. Perimeter v. Area

1.

Introductory Possibilities

  • 1. The Rects of Integer Equilateral Triangles
  • 2. The Rects of a Triangle's Perimeter (positive reals)
  • 3. Rect-Tri-Areas
  • 4. Overflowing Rectangles

1.1.

The Rects of Integer Equilateral Triangles

Can we use the perimeter of the triangle to enclose more area with a rectangle?
– Scott Farrar

1.2.

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1.3.

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1.4.

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2.

"Act 2" providing tools for exploration

What can students dig into with Geogebra, taking advantage of the continuous feedback possible?

  • 1. Area v. Perim for Quads and Tris
  • 2. 2 Rects 2 Furious

2.1.

Area v. Perim for Quads and Tris

Both polygons have a related coordinate point that plots its (perimeter, area). Change the size and shape of the quadrilateral and triangle, observe the change in the coordinate points. Can you find a triangle who's point is directly to the left of the quadrilateral's point? [url]www.scottfarrar.com[/url] | [url]https://twitter.com/farrarscott[/url]
– Scott Farrar

2.2.

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3.

Views of "the solution"

these show some answers to some of the possible questions that may arise

  • 1. Answer to Equal Perim and Area Triangle,Rectangle
  • 2. Answer 2 to Equal Area, Perim of Rectangle, Triangle
  • 3. Perimeter v. Area

3.1.

Answer to Equal Perim and Area Triangle,Rectangle

The triangle and rectangle have equal perimeters.[br][br]Drag point F onto K and the rectangle and triangle will also have equal areas.
Answer to Equal Perim and Area Triangle,Rectangle
– Scott Farrar

3.2.

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3.3.

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