http://www.ck12.org Chapter 10. Perimeter and Area
10.10 Area of a Circle
Here you’ll learn how to calculate the area of a circle.
What if you wanted to figure out the area of a circle with a radius of 5 inches? After completing this Concept, you’ll
be able to answer questions like this.
Watch This
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Click image to the left for more content.CK-12 Foundation: Chapter10AreaofaCircleA
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Click image to the left for more content.Brightstorm:Area ofCircles
Guidance
Recall thatπis the ratio between the circumference of a circle and its diameter. We are going to use the formula for
circumference to derive the formula for area.
First, take a circle and divide it up into several wedges, or sectors. Then, unfold the wedges so they are all on one
line, with the points at the top.
Notice that the height of the wedges isr, the radius, and the length is the circumference of the circle. Now, we need
to take half of these wedges and flip them upside-down and place them in the other half so they all fit together.
Now our circle looks like a parallelogram. The area of this parallelogram isA=bh=πr·r=πr^2.
To see an animation of this derivation, see http://www.rkm.com.au/ANIMATIONS/animation-Circle-Area-Derivatio
n.html, by Russell Knightley.
The formula for thearea of a circleisA=πr^2 whereris the radius of the circle.
Example A
Find the area of a circle with a diameter of 12 cm.
If the diameter is 12 cm, then the radius is 6 cm. The area isA=π( 62 ) = 36 πcm^2.