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Discovering Geometry: Area of Circles and Sectors with Special Right Triangles

Explore the ancient Babylonians' methods and modern systems to find the area of circles and sectors using special right triangles. Calculate areas based on given perimeters and circumferences for practical applications. Learn concepts for efficient traffic control and urban planning.

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Discovering Geometry: Area of Circles and Sectors with Special Right Triangles

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  1. ~Geometry 2~ Mr. Field Ms. Knoll Mr. Williamson Today’s Objectives Module 19:Identify special right triangles Module 20: Area of regular polygons and circles and circle sectors Ancient Babylonians

  2. Right hand driving • Systems of shared intersections • One-way traffic circles • One-way streets • Traffic signs • Pavement marking • Regulations against jaywalking • Taxi stands • Off-street parking • Driver’s licenses • Vehicle registration • Traffic tickets

  3. Goal: find the area of the circle. Area of sector is 20mm 45°

  4. The perimeter is 20 cm. Find the area.

  5. The perimeter is 24 cm. Find the area.

  6. The perimeter is 20 cm. Find the area. (using triangles)

  7. Red= Blue= r ?

  8. Find the area given the circumference is 22mm

  9. Find the area given the circumference is 30mm

  10. Goal: find the area of the circle. Area of sector is 20mm 45°

  11. Goal: find the area of the circle. Area of sector is 44mm 20°

  12. ~Geometry 2~ Mr. Field Ms. Knoll Mr. Williamson Today’s Objectives Module 19:Identify special right triangles needed for Mr. Field’s presentation on circles Module 20: Area of regular polygons and circles and circle sectors William Phelps Eno

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