The big picture
One idea is used again and again here: share, then subtract.
| Idea | Remember | Example |
|---|---|---|
| The share | Arc = θ/360 × 2πr. Sector = θ/360 × πr². | 90° of radius 7 → arc 11, sector 38.5 |
| Take the triangle away | Minor segment = sector − triangle. | 38.5 − 24.5 = 14 |
| Three triangles | 60°, 90°, 120° build from owned facts. | Areas 49√3/4, 49/2, 49√3/4 |
| The twins | The 60° and 120° triangles are equal, for the same radius. | Both 49√3/4 |
| Major pieces | Major sector = πr² − minor sector. Major segment = πr² − minor segment. | Quarter of radius 20, π = 3.14: major sector 942 |
| Reading a design | Name each round piece's share of the turn. Compute it. Then add or subtract it. | Medal card = 357 |
| The design decides | Add the round piece when it sticks out of the shape. Subtract it when it is cut out of the shape. | 273 or 119 |
| Walking the boundary | Count every outer edge once. A seam is not an edge. | 64 m |
This chapter is Areas Related to Circles. It is Chapter 11 of your Mathematics book. Find the sector, then take away the triangle. Most of this chapter uses that idea.