Sector Area
Part of the Angles and the Unit Circle section of Coddy's Trigonometry journey. Lesson 23 of 57.
A sector is a slice of the disc. Its angle θ is the fraction θ/(2π) of a full turn, so its area is that fraction of the whole disc, π×r^2. The π cancels:
A = 1/2×r^2×θ
The sector is π/3 out of 2π: one sixth of the disc.
With radius 6 and π/3: A = 1/2×6^2×π/3, which is 6π. Check it as a fraction: π/3 is a sixth of a turn, and a sixth of 36π is 6π. As with arcs, θ is in radians.
Challenge
A sector has radius 10 and angle 3π/5. On the blank board, write A with the numbers put into A = ½r²θ, then a line with A exact, as a multiple of π. Then press Check.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Angles and the Unit Circle
1A Point on a Circle
Height on the CircleAcross: the CosineSame Height, Two AnglesRecap: Height and Across4Radians
What a Radian IsDegrees to RadiansRadians to DegreesRadians Without πTurns in RadiansRecap: Radians5Arc Length and Sector Area
Arc LengthArcs From DegreesFinding the AngleSector AreaRecap: A Slice of Pizza