# 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

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

Relevance
• 8 years ago

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

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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