What do you do when you're finding the perimeter and area of a sector?

"Find the perimeter and area of a sector of:

a) radius 8cm and angle 40 degrees

b) radius 12cm and angle 2.4 radians

could someone explain the processes of how to do this? i don't quite understand.

2 Answers

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  • 8 years ago
    Favorite Answer

    a) Perimeter is the total distance around the two dimensional figure.

    If it is a circle , perimeter is the circumference.

    If it is a sector , then it is 2 X radius + length of the arc

    Radius = 8cm

    circumference = 2 X 3.14 X 8 = 50.24 cm

    Length of arc = 40/360 X 50.24 = 50.24 / 9 = 5.582 cm

    Perimeter = 2 X 8 + 5.582 = 21.582 cm ANSWER

    Area of circle = 3.14 X 8 X 8 = 200.96 cm^2

    Area of sector = 200.96 X 40 /360 = 200.96 /9 = 22.328 = 22.33 cm^2 ANSWER

    b) 1 radian is the angle subtended by an arc whose length is = to the radius

    There are 2*pi radians in a circle

    2*pi = 360

    1 radian = 180 / pi

    2.4 radians = 2.4 X 180 / pi = 137.58 degrees

    Perimeter of sector = ( 2 X 12 )+ ( 2 X 3.14 X 12 X 137.58/ 360)

    = 24 + 28.80 = 52.80 cm ANSWER

    Area of sector = 3.14 X 12 X 12 X 137.58 / 360 = 172.80 cm^2 ANSWER

  • Pranil
    Lv 7
    8 years ago

    Perimeter of sector = ø/360 × 2πr

    = 40/360 × 2 × 3.14 × 8

    = 5.58 cm

    Area of sector = ø/360 × πr²

    angle ø degree = radians × 180/π

    ø = 2.4 × 180/π

    Area of sector = ø/360 × πr²

    = 2.4 × 180/360π × π × 12²

    = 172.8 cm²

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