Find the area of the Tangram pieces


Goal: Review area of polygons, precision and rounding error

Primary Objective: The student will create a set of Tangrams, review/explore the area of polygons in metric units and work with different levels of precision in measurements.

Secondary Objective: The student will move (translate) or turn (rotate) pieces in the red green plane to create recognizable Tangram puzzles.

SketchUp Tools: Model Info unit settings, rectangle, zoom, pencil, paint bucket, text, group, move, rotate

Template: Open the Beginning Training Template - Meters.
This template will open in a birds-eye view of the red-green plane. The unit of measure is meters.
Tangram Window Info.jpg
Open Window | Model Info | Units
You will see the format, measurement, and precision for segment length.
The default setting is ten-thousandths of a meter 0.0000m.
For this activity, we will modify the precision to hundredths.
Angles are measured in degrees with a default precision set at tenths, 0.0.

Create Tangram Pieces:

Step 1. Use the Rectangle tool to draw a 1 meter by 1 meter square. You may use the red and green axis as guidelines. Type 1,1 into the status bar to force the dimensions of the square to 1 meter by 1 meter. Zoom in or out as needed to maximize the square on your screen (Zoom tools or scroll with your mouse wheel).

Step 2. Use the Line tool to draw the line segments needed to create the Tangram pieces. Use inference points to locate midpoints of segments.
Tangram Create.jpg

Step 3. Use the Paint Bucket tool to “paint” the Tangram pieces. Suggested colors listed here are found in the crayon box (macs)
a) Banana Yellow
b) Sky Blue
c) Carnation Pink

Step 4. Use the Text tool to label the areas of each piece of the Tangram puzzle. Snap the text tool to the interior of the piece (double click) and drag out with your mouse to position the area text (see the diagram).
Tangram Areas.jpg
Step 5. In this step, you will make each piece into a “group” so the pieces can be moved without deforming.
  • Select one piece and use the Edit | Group command to form a group.
  • Select another piece and use the Edit | Group command to form a new group.
  • Repeat this procedure to group all of the Tangram pieces.

Pause for Discussion Prompts:
1. Compute the area of each piece using fractions instead of decimals.
Hint: A sketch on paper might be helpful. Consider using a grid that divides the square into 16 pieces.

2. Confirm that the decimal areas given by SketchUp are equivalent to your fractional dimensions.
  • Explain why 0.13 + 0.13 does not equal ¼ of the square.
  • Does SketchUp round the area measurements or truncate them? Define these terms with an example.
  • Does the total area equal 1 square meter if you increase the precision to three decimal places in SketchUp?

Step 6. Use the Move tool to drag a piece to a new location in the red-green plane. This is called a translation. Use the Esc key to unselect a piece (if necessary).

Step 7. Use the Rotate tool to turn a piece clockwise or counterclockwise a given number of degrees.
  • Snap the center of the rotate tool to the center of the group for the shape.
  • Align the bottom of the protractor with one of the corners.
  • Note that angle measure will appear in the status bar of you drag the tool, or you can type in the angle you want to use.

Tangram Duck.jpg
Step 8. You might find that it is necessary to flip the parallelogram piece over.
  • Select the Scale tool and highlight the parallelogram.
  • Select one of the green points and set the scale factor to (-1) in the status bar.
  • This “flips” the piece over without changing the dimensions.

Save your file with the name Tangram_Yourname
Make some new shapes and submit them to this Wiki.
Sample File:

Updated May 2014