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Circumference, Area,
Surface Area, and Volume
By Taylor Winter
Derive the Formula:
Area of a Circle
Example Problems
1. A circle the radius of 4 cm. What is the area of the circle?
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Area of a circle= πr2
r= 4 cm
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4 cm x 4 cm = 16 cm^2
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16cm^2 x π
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The area of the circle is 16πcm^2
Similar to a regular polygon it can be broken up into equilateral triangles with one curved side. Using the additive and moving principles these 'triangles' can be arranged into a parallelogram.
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Then using the area of a parallelogram do base x height.
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Base is equal to half of the circumference since it is half of the curved sides of the original circle.
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Height is equal to the radius of the circle.
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1/2(2 x π x R)2
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The area of a circle is πr2.
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