More Tangram Activities

Objectives

a better understanding of area without formulas
the ability to compute the area of polygons by decomposition
a familiarity with the names of certain polygons
(e.g., rectangle, trapezoid, and pentagon)
the meaning of the term similar
to develop geometric intuition

Materials

a package of tangrams for each student
a student notebook
a sharp pencil
a ruler
an overhead projector

Primary activities

Knowing the area of each tangram piece from the previous lesson, the student can compute the area of any  polygon constructed from tangrams.

1. Make a square with the medium-size triangle and the two small congruent triangles. What is the area of this square? How do you know? Sketch the square in your notebook and record its area.

2. Make a rectangle with the parallelogram and the two small congruent triangles. What is the area of this rectangle? How do you know? Sketch the rectangle in your notebook and record its area.

3. Construct a triangle congruent to the large triangle shown below without using the small square. Sketch the large triangle in your notebook and record its area.
   

4. Make a square congruent to the square shown below without using a large triangle. Sketch the square in your notebook and record its area.
   

5. Construct a square using all seven tangram pieces. What is its area? How do you know? Sketch this large square in your notebook and record its area.

6. Find a trapezoid congruent to the trapezoid shown below. What is the area of this trapezoid? How do you know? Sketch the trapezoid in your notebook and record its area.
   

7. Find a trapezoid that is similar (but not congruent) to the trapezoid shown above. What is the area of this trapezoid? How do you know? Sketch the trapezoid in your notebook and record its area.

8. Find a pentagon congruent to the pentagon shown below. What is the area of this pentagon? How do you know? Sketch the pentagon in your notebook and record its area.
   

9. Find a pentagon congruent to the pentagon shown below without using the small square. What is the area of this pentagon? How do you know? Sketch the pentagon in your notebook and record its area.
   

Extended activities

1. Suppose the square constructed in activity 5 above has area one square unit. Determine the area of each tangram piece.

2. Repeat the previous problem assuming the large square has area twelve square units.

3. Measure the actual  area of each tangram piece.