Bradley G. answered • 09/19/19
Inspiring and Experienced K-12 and College Level Tutor
to find the area of a sector, you need to:
1) find the area of the circle
2) determine the percentage of the circle represented by sector arc measure (or central angle measure)
3) multiply the results from steps 1 and 2
per the above...
1) find the area of the circle
A = πr2
d = 10 therefore r = d/2 = 10/2 = 5
A = π52
= 25π
2) determine the percentage of the circle represented by sector arc measure (or central angle measure)
the percentage of circle represented by arc measure (central angle measure) = arc measure / 2π
percentage = (7π/6)/2π
= (7π/6)/(2π/1) invert and multiply
= (7π/6)*(1/2π) multiply across and simplify
= 7/12
3) multiply the results from steps 1 and 2
area of the sector = area of circle x percentage of circle represented by the arc
= 25π x 7/12
= 175π/12
= 14.58π units2
