Area of a Sector
Part of the Circles section of Coddy's Geometry journey. Lesson 17 of 62.
A sector is a slice of the circle, the region between two radii and their arc, like a slice of pizza. It takes the same share of the circle's area as its central angle takes of 360°.
Here the angle is 90°, a quarter of the turn. The whole circle has area π × 4² = 16π, so the sector is a quarter of it, 4π. The rule is A = t/360 × πr²: the same share as the arc length, taken of the area instead of the circumference.
Challenge
OA and OB are radii of circle O with the central angle marked. Find the area of the sector OAB, exact in terms of π, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Circles
1Parts of a Circle
Center and RadiusChords and DiametersAll Radii Are EqualDiameter Is Two RadiiRecap: Parts of a Circle4Arcs and Sectors
Arc LengthArea of a SectorFind the Central AngleThe Missing Central AngleRecap: Arcs and Sectors2Circumference
Around the CircleUsing the DiameterRadius From CircumferenceCircumference With LettersRecap: Circumference5Radii Make Isosceles
Two Radii, One TriangleBase Angles From the CenterThe Angle at the CenterIsosceles With LettersRecap: Radii and Triangles8Angles on the Same Arc
Same Arc, Same AngleUsing the Same ArcSpot the Bow TieSame Arc With LettersRecap: Same Arc3Area of a Circle
The Area FormulaArea From the DiameterRadius From the AreaCircumference to AreaRecap: Area of a Circle6Inscribed Angles
Meet the Inscribed AngleHalf the Central AngleTwice the Inscribed AngleThe Big ArcInscribed With LettersRecap: Inscribed Angles