1. Exploring Area of Polygons

2. Exploring the Area of a Parallelogram
Objective: Students will derive the formula
for the area of a parallelogram.
Materials:
Index Cards
Ruler
Scissors
Tape

3. Step 1: Find the Area of your index card.

4. Step 2: Use a straightedge to draw a line through one of the vertices of your index card.

5. Step 3: Cut out the triangle
Step 3: Cut out the triangle. Tape the triangle to the opposite side to form a parallelogram.

6. Think About It
How does the area of the parallelogram compare
to the area of the rectangular index card?

7. Think About It
2. How do their bases compare?
3. How do their heights compare?

8. Think About It
Write a conjecture about the formula for the area
of a parallelogram.

9. Exploring the Area of a Triangle
Objective: Students will derive the formula
for the area of a triangle.
Materials:
Grid paper
Colored pencils or markers
Scissors

10. Step 1: Draw a triangle on grid paper
Step 1: Draw a triangle on grid paper. Then draw a rectangle that encloses the triangle. Write down the dimensions of the rectangle.

11. Step 2: Cut out the rectangle
Step 2: Cut out the rectangle. Then cut the triangles out of the rectangle.

12. Step 3: Arrange the two smaller triangles to cover the area of the large triangle .

13. Think About It
Do the two smaller triangles cover the same
area as the large triangle?

14. Think About It
2. How is the area of the large triangle related to
the area of the original rectangle?

15. Think About It
Use the dimensions of the rectangle in step 1
to find the area of the rectangle, then use your
answer to find the area of the large triangle.

16. Use the diagram below to write a conjecture
about the area of a triangle given its
base b and its height h.

17. Exploring the Area of a Trapezoid
Objective: Students will derive the formula
for the area of a trapezoid.
Materials:
Grid Paper
Ruler
Scissors
Tape

18. Step 1: On grid paper, cut out two identical trapezoids
Step 1: On grid paper, cut out two identical trapezoids. Label the bases b1 and b2, respectively, and label the heights h.

19. What is the shape formed by the two identical trapezoids?
Step 2: Then turn one trapezoid upside down and tape it to the other trapezoid as shown
What is the shape formed by the two
identical trapezoids?

20. Think About It
Write an expression to represent the base of
the parallelogram you created.

21. Think About It
2. Write an expression to represent the area of the
parallelogram you created.

22. Think About It
How does the area of each trapezoid compare
to the area of the parallelogram you created?

23. Think About It
Write a conjecture about the formula for the
area of the trapezoid.

24. Exploring the Area of a Circle
Objective: Students will derive the formula
for the area of a circle.
Materials:
Paper
Compass
Ruler
Scissors

25. Step 1: Use a compass to draw a circle on a piece of paper
Step 1: Use a compass to draw a circle on a piece of paper. Cut the circle out. Fold the circle in half, four times.

26. Step 2: Cut the circle along the fold lines to divide the circle into 16 equal wedges.

27. Step 3: Arrange the wedges to form a shape resembling a parallelogram
Step 3: Arrange the wedges to form a shape resembling a parallelogram. The base and height of the parallelogram are labeled.

28. Think About It
1. How does the area of the original circle compare
to the area of the parallelogram you created?

29. Think About It
2. Write an expression for the height of the
parallelogram you created.

30. Think About It
3. Write an expression for the base of the
parallelogram you created.

31. Think About It
4. Write an expression for the area of the
parallelogram you created.

32. Think About It
5. Use the fact that to rewrite the area.

33. Think About It
6. Use the fact that to rewrite the area.

34. Think About It
Write a conjecture about the formula for the
area of a circle.

35. NCTM-Circle Lesson
Circle Applet