Project AMP
Dr. Antonio Quesada – Director, Project AMP
Finding the Area of a Parallelogram with Translations
Key Words:
Area, Parallelogram, Translation, Parallel lines, Base, Perpendicular, Height, Plane,
Altitude, and Reflection
Existing Knowledge:
Students should be familiar with the Cabri Geometry II program.
They should have an understanding of measuring length, calculating area of rectangles
and triangles, recognizing perpendicular, parallel, and diagonal lines, and identifying the
transformation of a figure.
NCTM Standards :
Students will analyze characteristics and properties of two and three-dimensional
geometric shapes and develop mathematical arguments about geometric relationships.
Learning Objectives:
The students will classify quadrilaterals, understand the relationship between twodimensional figures, recognize perpendicular and parallel segments and find the area of
two-dimensional figures.
Materials:
Cabri II Geometry Program
Lab Worksheets
Computer or Graphing Calculator
Paper and scissors (optional)
Math text (as resource)
Procedure:
þ Students should be placed in groups of 2-4.
þ The teacher will demonstrate the process of translating, rotating, and reflecting an
interesting shape on the overhead screen. Ask students for real life examples of these
ideas: footprints in the sand, wallpaper print, artwork, and so on
þ Inform students that they will investigate the area of a parallelogram using a
translation.
þ Distribute the lab worksheets and instruct the students to begin the Cabri II program.
þ Those students, who need the extra support, may use the scissors and paper to
reinforce the idea.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Finding the Area of a Parallelogram with Translations
Lab Worksheet
Name________________________________________________________________
1. Draw a rectangle.
(Polygon tool)
2. Estimate the area______, then measure the exact area.
(Area Tool)
3. Draw a non-rectangular parallelogram.
(Polygon tool)
4. Estimate the area. ________________
Find the area._________________. Clear the screen.
(Area tool)
5. Construct a set of parallel lines.
(Parallel line tool)
6. Label the first line m and the second line n.
(Label tool)
7. Place point A on the first line and point B on the bottom line.
(Point tool)
8. Draw AB .
(Segment tool)
9. Create a parallel line to AB .
(Parallel line tool)
10. Label the intersection points, C on first line and D on second line.
(Point tool)
11. Draw segments AB , AC , CD and BD .
(segment tool)
12. Hide all lines outside of the parallelogram.
(hide/show tool)
13. Draw a perpendicular line from point A to
the line below point A.
14. Create BD. Place a point E at the intersection of BD.
9.
Draw segment AE and hide the line outside of the figure.
(segment tool)
(Perpendicular tool)
Project AMP
Dr. Antonio Quesada – Director, Project AMP
10. Measure the height AE and base BD.
(measure tool)
11. Draw triangle ABE over the segments. Fill the triangle with any color.
tool)
12. Translate triangle ABC by drawing a vector from A to B.
(translation tool)
Click the triangle and touch the vector.
(vector tool)
Delete the original triangle.
13. How does the height of the rectangle, formed by sliding the triangle, compare
to the height of the original parallelogram?
______________________________________________________________
14. What is the area of the rectangle?___________
(area tool)
15. Estimate the area of the original parallelogram.__________
16. Repeat steps 2-12, using a non-rectangular parallelogram of a different size.
17. Compare your results to what you discovered about the first parallelogram.
____________________________________________________________
____________________________________________________________
____________________________________________________________
18.
State a general rule for finding the area of a parallelogram. _____________
_____________________________________________________________
The area of a RECTANGLE is A=l*w or A=b*h
for a PARALLELOGRAM A=b*h and for a TRIANGLE A=1/2b*h
EXTENSION:
19. Clear the screen. Construct two congruent triangles. Rearrange them to form a
parallelogram.
20. How does the area of each triangle compare to the area of this new parallelogram?
(fill