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A rangoli petal is a thin curved piece. It is not a whole wedge of the circle.

This is Chapter 11: Areas Related to Circles. It takes a circle apart, piece by piece, and measures every piece.

What you will learn

• The share again — arc and sector, at any angle, one π.
• Take the triangle away — a chord leaves a segment behind.
• Three angles, three triangles — 60°, 90°, 120° build from facts you know.
• The quarter-turn segment — measured whole, with a clean walk round it.
• The twin segments — 60° and 120° give the same triangle area.
• Reading a design into pieces — a badge splits into measured pieces.
• The design decides — the same pieces are added on or taken away.
• Walking the boundary — arcs and straight lines, taking turns round the edge.

Need a quick recap?

Six earlier lessons matter most here. If one feels unsure, tap it and revise it.

• A piece of the edge — an arc's share of the way round.
• Wedges, and a rectangle they approach — a circle's area, by the radius.
• A slice of the inside — a sector's share of the area inside.
• Four names, four parts — chord, arc, segment and sector.
• Awkward outlines, ordinary pieces — no formula splits into shapes that do.
• The two smaller squares together — the right triangle's two shorter sides.