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Area of a Sector

Area of a Sector
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2017-01-13 16:52
CircleAngleGeometric Construction
This example demonstrates how to determine the area of a sector by rotating and measuring the central angle. Key mathematical concepts include the properties of circles and angle measurement. It uses commands such as Circle, Point, Segment, Rotate, Angle, CircleSector, Area, and PointIn in GeoGebra. Suitable for middle school and above students to learn geometric construction and area calculation.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → B
  3. Segment(A, B) → f
  4. Rotate(B, α, A) → B'
  5. Angle(B, A, B') → α_2
  6. Segment(A, B') → g
  7. CircleSector(A, B, B') → d
  8. Area(d) → b
  9. PointIn(d) → Pointd
  10. Area(c) → e
  11. PointIn(c) → Pointc

AI Drawing Prompt Reference

Draw a circle and mark its center and a point on the circle. Connect these two points to form a line segment. Rotate the segment around the center by a certain angle to get another point, then connect the center to this new point. Create a sector using the center and the two points, and calculate its area. Also, calculate the area of the entire circle. Mark points on both the circle and the sector to demonstrate the relationship between the area calculations and the shapes.
The prompt above was compiled from the original drawing commands and is for reference only.