Compose the leftover region
A square has four quarter-circles cut from the corners. Change the side length and watch the leftover area follow square minus one full circle.
A square with quarter-circles bitten from every corner looks like a flower. The trick: four quarter-circles stitched together = one full circle, so the leftover area = side² − πr². Change the side and watch the leftover scale.
Aligned with CCSS 7.G.B.4.
Four quarters make one full circle, then subtract from the square.
Side 6, radius 3: square minus one full circle.
Geometry and measurement model
Four Quarter-Circles in a Square is built for students who memorize formulas before seeing the shape decomposition. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Four Quarter-Circles in a Square helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
Learning goals
How to play
Continue with guided practice
Each quarter has area ¼ πr². Four quarters sum to πr² — the area of one full circle of the same radius.
6² − π × 3² = 36 − 9π ≈ 7.73 cm². The four corners merge into a curvy petal-shaped region in the middle.
Because both side² and πr² are quadratic. Scaling lengths by 2 scales every area by 4 — including the leftover.
Grades 6–7, aligned with CCSS 7.G.B.4. Classic composite-figure pattern.
