Area of Tangram Pieces: Part A
Complete all questions or statements below. Show your work on your own piece of paper.
1.
Trace the small square in your notebook. Let's suppose this square has area
one square unit. Write "one square unit" next to the small square.
2.
Make a square with the two small congruent triangles. What is the area of
this square? How do you know?
3.
Trace one of the small triangles in your notebook. What is the area of this
triangle? How do you know? Write the area next to the small triangle.
4.
Trace the parallelogram in your notebook.
5.
Make a (non-square) parallelogram with the two small congruent triangles.
What is the area of this parallelogram? How do you know? Write the area
next to the parallelogram.
6.
Trace the medium-size right triangle in your notebook.
7.
Make a triangle with the two small congruent triangles. What is the area of
this triangle? How do you know? Write the area next to the medium-size
triangle.
8.
Trace one of the large triangles in your notebook.
9.
Make a triangle with the small square and the two small congruent triangles.
What is the area of this triangle? How do you know? Write the area next to
the large triangle.
10. Make a square with the two large congruent triangles. What is the area of
this square? How do you know?
Area of Tangram Pieces: Part B
Complete all questions or statements below. Show your work on your own piece of paper.
Using the area of each tangram piece from the previous lesson, you can compute the area of any polygon
constructed from tangrams.
11.
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.
12.
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.
13.
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.
14.
Make a square congruent to the square shown below without using a large triangle. Sketch the
square in your notebook and record its area.
15.
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.
16.
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.
17.
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.
18.
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.
19.
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.
Extension
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.