The Area Formula
Part of the Circles section of Coddy's Geometry journey. Lesson 11 of 62.
The area of a circle is the space inside it: A = π×r^2. To see why, cut the circle into many thin slices like a pizza and lay them side by side, points up and points down. They form a shape that is almost a rectangle. Its height is the radius, and its length is half the circumference, πr. Length times height is πr × r = πr².
Here the radius is 3, so the area is π × 3² = 9π. Square the radius first, then keep π as π. Area is in square units, so 9π square centimeters if the radius is in centimeters.
On the board, tap inside the circle, choose its area, and pick Area of a circle.
Challenge
Circle O has radius 7. Find its area A, 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