1. Area of Circles with Exercises
Geometry
Regular Program SY
Sources:
Discovering Geometry (2008) by Michael Serra
Geometry (2007) by Ron Larson

2. CIRCUMFERENCE vs. AREA
Imagine a string that will be wrapped around a coin, or wheel (without overlaps). The length of that string determines the circumference of the circular object.
In any circle, the ratio Circumference over diameter is constant.
This ratio is known as pi.
Pi is equal to …

3. How do we get the area of a circle?
A circle can be separated into smaller parts that resemble a “pizza slice”.

4. How do we get the area of a circle?
A circle can be separated into smaller parts that resemble a “pizza slice”.

5. How do we get the area of a circle?
Half of circumference
Rearrange the pieces to form a “paralellogram”.

6. Area of Circles and Parts

7. Area of Circles and Parts

8. Area of Circles and Parts

9. Area of Circles and Parts

10. Area of Circles and Parts
Example:

11. Area of Circles and Parts
Example:

12. Area of Circles and Parts
Example:

13. Determine the area of the shaded region.
Half of circumference

14. Determine the area of the shaded region.

15. Determine the area of the shaded region.

16. Determine the area of the shaded region.

17. Determine the area of the shaded region.

18. Determine the area of the shaded region.

19. Determine the area of the shaded region.

20. Determine the area of the shaded region made up of semicircles.

21. Determine the area of the shaded region.
The arcs are from a circle with radius of 6cm.
The quadrilateral is a square.

22. Which shaded region has a greater area?

23. Determine the area of the shaded region.

24. Determine the area of the shaded region.

25. Determine the area of the shaded region.