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Tetrahedral Kites

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    NCTM Illuminations

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Tetrahedral Kites

In this math lesson, each learner constructs a tetrahedron and describes the linear dimensions, area and volume using non‑traditional units of measure. Four tetrahedra are combined to form a similar tetrahedron, whose linear dimensions are twice the original tetrahedron. The area and volume relationships between the first and second tetrahedra are explored, and generalizations for the relationships are developed. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

Quick Guide

Preparation Time:
Under 5 minutes

Learning Time:
1 to 2 hours

Estimated Materials Cost:
$1 - $5 per group of students

Age Range:
Ages 11 - 18

Resource Types:
Activity, Lesson/Lesson Plan


Materials List (per group of students)


  • Mathematics
    • Geometry
      • Plane Geometry
      • Solid Geometry
    • Measurement
      • Polygons
  • Physical Sciences
    • Structure and Properties of Matter
      • Volume and Density

Informal Categories

  • Arts and Crafts
  • Toys


To use this activity, learners need to:

  • see
  • read
  • touch

Learning styles supported:

  • Involves teamwork and communication skills
  • Involves hands-on or lab activities


Includes alignment to state and/or national standards

Common Core State Standards for Mathematics:

  • CCSS.Math.Content.6.G.A.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.(more info about this benchmark)
  • CCSS.Math.Content.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.(more info about this benchmark)
  • CCSS.Math.Content.HSG-CO.D.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.(more info about this benchmark)
  • CCSS.Math.Content.HSG-GMD.B.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.(more info about this benchmark)

Includes assesments for student learning

Access Rights:

  • Free access


  • Warloe, Kris A.


  • All Rights Reserved, National Council of Teachers of Mathematics, ©2008

Funding Source:

  • Thinkfinity/Verizon Foundation


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