Perimeter of a sector includes the two radii
Perimeter — don't forget the straight edges.
A sector is a fraction of the whole circle
The fraction is . Arc length ; sector area .
Drawn from real examiner reports.
Perimeter: forgetting the two radii
The perimeter of a sector is the arc length plus the two straight radii (). Giving only the arc length, or leaving off , undercounts the perimeter.
Rearranging the area formula incorrectly
When solving for or , algebra slips are common; keep the fraction intact while rearranging.
Seen in examiner reports.
Sector area vs triangle or segment
Some find a triangle area or subtract values that the question did not ask for.
Seen in examiner reports.
Arc length vs sector area
Arc length uses the circumference ; sector area uses . Multiplying the wrong one by — a length when an area is asked for — is a frequent error.
Radius or diameter mix-up
Both formulas use the radius . If a diameter is given, halve it first; substituting the diameter for doubles the arc length and quadruples the area.
Write the formula, substitute, then evaluate
Show the substitution before pressing buttons — it earns method marks even if the arithmetic slips.
Work out the fraction θ/360 first
Find first, then multiply by for an arc or for a sector. Keeping it as one factor makes reverse problems (finding or ) easier to rearrange.
Keep θ/360 intact when rearranging
To find or , substitute the known values then rearrange, keeping as a single fraction. Splitting it up mid-rearrangement is where algebra slips creep in.
For a sector of radius with angle (in degrees):
Both are just the fraction of the whole circle.
What fraction of the circle is a sector?
A sector has radius cm and angle . Find its area, correct to 1 d.p.
