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: Use Construction Documentation - Meters

This template will open in a birds-eye view of the red-green plane. The unit of measure is meters.

Open Window | Model Info | Units

You will see the format, measurement, and precision for segment length.

For this activity, we will use hundredths (the default setting).

Angles are measured in degrees with a default precision set at tenths.

Online version: Views - the middle option is a top view

Online version: Units - select meters and two decimal places

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.

Step 5. In this step, you will make each piece into a “group” so the pieces can be moved without deforming.

Online version, I had to select the piece (surface) and the edges of that piece for the Group command to appear. Hot keys are ctl + shift to select all the pieces.

• Delete each of the area measures.
• 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.

Online version: The areas are 0.12 meters instead of 0.13 meters. What is going on here?

• Explain why 0.13 + 0.13 does not equal ¼ of the square.
• Define truncate.
• Does SketchUp round the area measurements or truncate them?
• 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 7a. 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 of the shape yoU want to rotate. [You might need to draw a segment in the shape to locate the center. Delete this segment after the rotation is completed.]
• Align the "bottom" of the protractor with one of the corners.
• Note that the angle measure will appear in the status bar as you drag the tool, or you can type in the angle you want to use.

Step 7b. Select the shape, select the move tool, select one of the + signs that appear. Rotate the shape as necessary.

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 - Be prepared to submit the file electronically.

Updated August 2017