calculate thetotal perimeter of the sector
P(rectangle) = 2L + 2W
The perimeter is the distance around a figure.
if it's a circular sector, then it's 2r+s
where s is the arc length subtended.
To calculate the total perimeter of a sector, you will need three pieces of information: the radius of the sector (denoted by 'r'), the central angle of the sector (denoted by 'θ'), and the arc length of the sector (denoted by 's').
The formula to calculate the total perimeter of a sector is:
Perimeter = 2r + s
Where:
- '2r' represents the sum of the lengths of the two radii
- 's' represents the arc length
To find the arc length 's', you can use the formula:
s = (θ/360) × 2πr
Where:
- 'θ' is the central angle in degrees
- '2πr' is the circumference of the whole circle with radius 'r'
So, the steps to calculate the total perimeter of a sector are as follows:
1. Determine the radius of the sector ('r').
2. Determine the central angle of the sector ('θ') in degrees.
3. Calculate the arc length ('s') using the formula: s = (θ/360) × 2πr.
4. Calculate the total perimeter of the sector using the formula: Perimeter = 2r + s.
Remember to check your units and convert them if necessary (e.g., from degrees to radians) in order to have consistent measurements for calculations.