Perimeter of a circle. Area of a circle

Circle

  • The part of the circle bounded by two points lying on it is called a circular arc;
  • The part of a circle bounded by a circle and any two semicircles is called a circular section;
  • The part of a circle bounded by a circle and one of its tendons is called a circular section


Fig. 1


1. Perimeter of a circle and area of a circle

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Fig. 2


2. Area of parts of the circle

  • The area of a circular section is calculated by the formula:

223-f1

224-c12Fig. 3

  • Circular arc "l" can be calculated by the following formula:

  • If we know the circular arc, then the area of the circular section can be calculated with the following formula:

224-f1

  • For more advanced mathematicians who can solve integrals, perimeter and area can be calculated using the following formulas:

  • The area of a circular section can be calculated as the difference between the area of a circular section and the isosceles triangle formed by the two semicircles and the tendon. Given the area of this triangle which, expressed through the known quantities r and α, is:

  • The area of a circular ring is calculated by the formula:

225-c14

Fig.4


  • Video lesson – Perimeter of a circle and area of a circle

– perimor na kruznica i plostina na krug –

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