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.

The Area of a Circle Developed by Ivan Seneviratne

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.

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,

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

PRESTO !

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

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

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

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

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.

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

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

This presentation is developed by Ivan Seneviratne © 2007 purely for personal use.