Perimeter Problems Including Arcs
Grade 5Perimeter of a sector
The perimeter of a sector is not just the arc — it includes the two radii as well.
Sector perimeter = arc length + 2r
It is easy to forget the straight edges. Slow down, sketch the shape, and trace the full boundary.
Compound shapes with arcs
When a shape mixes straight sides with semicircles or quarter-circles, work out each piece separately: straight edges by measurement, curved edges using the arc length formula, then add everything.
A semicircle's perimeter contribution is πr (half the circumference), not the diameter. Add the diameter separately if it forms part of the straight boundary.
Worked example
EXAMPLE
A running track has two straight sections each 80 m long and two semicircular ends each with diameter 60 m. Find the total perimeter of the track.
Each semicircle has radius 30 m. Circumference of one full circle = 2π × 30 = 60π m. Two semicircles = one full circle = 60π m. Two straight sections = 2 × 80 = 160 m. Total perimeter = 160 + 60π ≈ 160 + 188.5 = 348.5 m (to 1 d.p.).
