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**How to calculate the area of a circle.**

It’s as easy as pi.

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**Let’s first make sure that we understand the difference between circumference and area.**

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**The circumference of a circle is the perimeter of the circle.**

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**Imagine that the circle is straightening itself out.**

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**The length of this line segment is the circumference of the circle.**

314 cm

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**The circumference is the same length as 3 diameters plus**

The circumference is the same length as 3 diameters plus .14 of another diameter.

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**So, circumference = diameter x 3.14**

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**Does this look familiar?**

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**O.K., now it’s time to move forward with some new stuff.**

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**How in the world would you find the area of a circle?**

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**Remember, area is always measured in square units.**

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Remember that the area of a rectangle is length x width because you’re calculating the total number of squares inside of the rectangle. 2 4

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**That’s fine and dandy, but a circle is not a polygon**

That’s fine and dandy, but a circle is not a polygon. It does not have straight sides; it has curves.

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**How are we going to get around these curves?**

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**Imagine chopping up the circle as if it were a pizza.**

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**Now, let’s rearrange our “pizza” into another shape.**

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PRESTO!

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**Great Mr. Dunlap! But what in the world is this?**

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**Believe it or not, this is really our “friend” the parallelogram**

Believe it or not, this is really our “friend” the parallelogram. And, we know how to calculate the area of a parallelogram.

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**Rats! He always has an answer for everything.**

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Area = Base x Height Height Base

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To find the area of the circle (which is now a parallelogram), we just need to multiply the Base by the Height. Height Base

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**Wait a minute! The height of this “parallelogram” is really the radius of the circle.**

Base

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**Wait a minute! The Base is really 1/2 of the circumference.**

Radius 1/2 of Circumference

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**Wait a minute! The circumference is really Diameter x **

Radius 1/2 of Diameter x

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**Wait a minute! 1/2 of a Diameter is really a Radius.**

Radius x

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**So if we multiply the Base x Height**

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**We are really multiplying Radius x Radius x **

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Practice Time!

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**1) Now let’s try this formula. Find the area of this circle.**

5 cm

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5 x 5 x 3.14 = 78.5 square cm 5 cm

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**2) Find the area of this circle.**

6 cm

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6 x 6 x 3.14 = square cm 6 cm

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**3) Find the area of this circle.**

9 cm

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9 x 9 x 3.14 = square cm 9 cm

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**4) Find the area of this circle.**

20 cm

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**Make sure that you use the radius of the circle.**

10 x 10 x 3.14 = 314 cm2 Make sure that you use the radius of the circle. 20 cm

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**5) Find the area of this circle.**

14 cm

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**Make sure that you use the radius of the circle.**

7 x 7 x 3.14 = cm2 Make sure that you use the radius of the circle. 14 cm

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**6) Find the area of this circle.**

22 cm

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11 x 11 x 3.14 = cm2 22 cm

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**Area = Radius x Radius x **

It’s as easy as pi.

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Perimeter & Circumference Return to table of contents.

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