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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 .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. 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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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.
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
Base
Height
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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.
Base
Height
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Base
Radius
Wait a minute! The height of this “parallelogram” is really the radius
of the circle.
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1/2 of Circumference
Radius
Wait a minute! The Base is really 1/2 of the circumference.
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1/2 of Diameter x
Radius
Wait a minute! The circumference is
really Diameter x
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Radius x
Radius
Wait a minute! 1/2 of a Diameter is really a Radius.
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Base
Height
So if we multiply the Base x Height
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We are really multiplying
Radius x Radius x
Radius x
Radius
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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 = 113.04 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 = 254.34 square cm
9 cm
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4) Find the area of this circle.
20 cm
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10 x 10 x 3.14 = 314 cm2
20 cm
Make sure that you use the radius of
the circle.
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5) Find the area of this circle.
14 cm
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7 x 7 x 3.14 = 153.86 cm2
14 cm
Make sure that you use the radius of
the circle.
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6) Find the area of this circle.
22 cm
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11 x 11 x 3.14 = 379.94 cm2
22 cm
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Area = Radius x Radius x
It’s as easy as pi.