Arc Lengths Problems

The perimeter of a shape with a curved edge is still the total distance around the outside. In NSW Year 8 maths (NESA outcome MA4‑LEN‑C‑01) a sector has a perimeter of its arc plus two radii, \(P = \frac{\theta}{360} \times 2\pi r + 2r\), with semicircles and quadrants as special cases.

You will find the perimeters of sectors, quadrants, the shape left when a slice is cut out, and composite figures made of straight sides, semicircles and arcs, leaving out any line drawn inside the shape. You will also work backwards from a perimeter to a radius or an angle, and cost timber edging for a sandpit or ribbon for a paper fan, rounding up to whole metres. It is part of Year 8 Area and Perimeter.