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.
 Make a square with the mediumsize 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.
 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.
 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.
 Make a square congruent to the square shown below
without using a large triangle. Sketch the square in
your notebook and record its area.
 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.
 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.
 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.
 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.
 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
 Suppose the square constructed in
activity 5 above has area one
square unit. Determine the area of each tangram piece.
 Repeat the previous problem assuming the large
square has area twelve square units.
 Measure the actual area of each
tangram piece.
