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ZingPath: Area and Circumference

Formula for the Area of a Circle

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Area and Circumference

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Formula for the Area of a Circle

Geometry

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The formula for the area of a circle is derived from the formula for the area of a parallelogram.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Derive the formula for the area of a circle.

Everything You'll Have Covered

In order for students to successfully complete this Activity Object, they should be familiar with the following shapes and their attributes:

  • circle - the locus of all points that are at an equal distance from a given point called the center.
  • circumference - the complete distance around a circle.
  • radius - the length of a line segment that connects the center of circle to any point on the circle.
  • parallelogram - a quadrilateral whose opposite sides are parallel and equal and opposite angles are equal.

Also, students should have a basic understanding of area.

  • area - the number of square units that cover a closed figure.
  • area of a parallelogram = , where b = base length and h = height
  • area of a circle = ?rē, where r = radius. This formula can be derived from slicing the circle and rearranging the pieces into a parallelogram. The arranged slices will leave an empty space, but as the number of slices increases, that empty space decreases. As that empty space decreases, the area of the sum of the slices (which is also the area of the circle) approaches the area of the parallelogram.

NOTE: This Activity Object uses '3.14' as a measurement for ?.

Once the slices of the circle have been rearranged, the radius of the circle becomes the height of the parallelogram. Likewise, half of the circumference becomes the length.

Tutorial Details

Approximate Time 15 Minutes
Pre-requisite Concepts Students should know the attributes of circles and parallelograms, and should be able to calculate the area of a parallelogram.
Course Geometry
Type of Tutorial Visual Proof
Key Vocabulary area, circle, parallelogram