1. Lesson Objectives 1.You will gain a deeper understanding of the fundamental concept of area of a circle. 2.You will understand how the formula for the area of a circle was determined. 3.You will demonstrate how to measure the area of a circle.

2. The Area of a Circle Developed by Ivan Seneviratne

3. How in the world would you find the area of a circle? The Area of a circle refers to the number of square units within the circle. Remember, area is always measured in square units.

4. Archimedes of Syracuse Calculating the area of a circle presented a major problem for the mathematicians of Archimedes' time. Archimedes of Syracuse proved that the area of a circle was equal to  multiplied by the square of the radius of the circle in “The Measurement of a Circle.” Archimedes Screw,

5. Archimedes’ Method Imagine chopping up the circle as if it were a pizza.

6. PRESTO !

7. Length Height So, What Now! To find the area of the circle which is now a parallelogram, we just need to multiply the length by the Height. Area = Length x Height

8. Wait a Minute! The height of this “parallelogram” is really the radius of the circle. The length is really 1/2 of the circumference. One half of circumference Radius Area = one half of circumference x Radius

9. Now What! The circumference is really  x Diameter and the diameter is twice the radius. One half of circumference Radius Area = ½ x  x Diameter x Radius = ½ x  x 2 x Radius x Radius

10. Area =  x Radius x Radius =  x r x r =  x r 2 It’s As Easy As Pi!

11. Area of a Circle The area of a circle is the region enclosed by the circle. It is given by the formula: A =  x r 2 where A is the area and r is the radius.

12. Now Let’s Try This Formula Find the area of this circle. 5 cm

13. Now Let’s Try Again Find the area of this circle. 10 cm

14. This presentation is developed by Ivan Seneviratne © 2007 purely for personal use. ivanthexplorer@yahoo.co.uk