1. Discovering
Area of a
Circle

2. Area of a Circle Discovery
For Learning to Happen:
Pay close attention to this lesson.
Listen to my instructions to discover the area of a circle formula.

3. Area of a Circle Discovery
You are going to get a white half sheet.
Label the circumference, diameter and radius on your circle.

4. Area of a Circle Discovery
Circumference
Diameter
Radius
Carefully cut out the circle on the black line.

5. Area of a Circle Discovery
Cut out the circle on the bolded lines.
Cut along the diameter to cut the circle in half.
You should have 2 halves.

6. Area of a Circle Discovery
Start from the diameter and cut the 4 pieces.
DO NOT CUT IT TO THE EDGE!
Open the semicircles and bend them out so they look like 4 connected triangles.

7. Area of a Circle Discovery
Fit the 4 triangles together so that as one is facing up, the other is facing down.
Tape these pieces together on your blue study guide handout.
Make sure your words on facing up!
radius
Circumference

8. Area of a Circle Discovery
Answer the following questions.
What does your new figure look like?
Parallelogram
2a. Draw your answer here. Label base & height
2b. How do you find the area of a parallelogram?
Base x Height
height
base

9. Area of a Circle Discovery
3. Draw your area of a circle figure below. In knowing that you need to find the base and height of your new figure to calculate the area, what is the height of your new figure? Label your picture.
4. What is the bottom base of your new figure? Label your picture above. Hint: Half of the circumference.
Height = radius
pi x radius

10. Area of a Circle Discovery
If you know the base and height of your new figure can you find the area? Take your base and multiply it by your height. Show your work!
6. Simplify your formula.
7. Write out how you find the area of a circle.
Pi times radius squared.

11. Area of a Circle Discovery
Here is what we just did:
We labeled everything.
Area = base times
the height. r r
radius
Circumference is
the distance
around the circle.
We cut our circle
in half making two
pieces.

12. Area of a Circle Discovery
Watch what happens when we use a circle with 16 triangles instead of using a circle with 8 triangles. r r
Notice that with more triangles the figure begins to really resemble a parallelogram. Area of a parallelogram is base times height.

13. Area of a Circle Discovery
Take out a calculator to try to solve the following problems on area of a circle.

14. Area of a Circle Discovery
6 in.
Find the area of the circle.

15. Area of a Circle Discovery
11 m.
Find the area of the circle.

16. Find the area of the circle.
Area of a Circle Discovery
What is the radius if the diameter is 10 ft?
10 ft.
Find the area of the circle.

17. Take out your study guide!
Area of a Circle Discovery
That's all Folks!
The End!
Take out your study guide!
That’s all folks

18. copyright©amberpasillas2010
Area of a Circle #7
6 in
= 3.14 or 22 7
copyright©amberpasillas2010

19. Given the Radius of a Circle#8
Given the Radius of a Circle
Round to the nearest hundredths place and include units!
5 ft
Find the Circumference
Find the Area
copyright©amberpasillas2010

21. Use this as a master to give to students
for the interactive discovery of a circle along with a copy of the worksheet.
Student materials for interactive discovery of a circle: Copy of circle pictured above, copy of area worksheet in this folder, scissors & tape.

22. Area of a Circle Area of a Circle
Follow the teacher directions and cut the circle out.
Area of a Circle
Follow the teacher directions and cut the circle out.

23. TEACHER NOTE: Give each student a copy of this page
TEACHER NOTE: Give each student a copy of this page. The master copy is in the folder as a pdf.