Formula sheet
Area of sector
(θ/360°) × πr² is given on the exam formula sheet. You must still know it is a fraction of the full area, that it uses πr² (not 2πr), and that θ is the centre angle in degrees.
What the symbols mean
- θ Angle at the centre of the sector, in degrees.
- r Radius of the circle (length unit).
- π Pi ≈ 3.142 or 22/7.
Given in the exam, or memorise?
(θ/360°) × πr² is given on the exam formula sheet. You must still know it is a fraction of the full area, that it uses πr² (not 2πr), and that θ is the centre angle in degrees.
Why it works
A sector is a fraction of the whole circle's area.
- The whole circle spans 360° and has area πr².
- A sector of angle θ covers the fraction θ/360°.
- So area of sector = (θ/360°) × πr².
Worked example 1
Find the area of a sector with centre angle 90° in a circle of radius 7 cm. (Use π = 22/7)
- Area = (θ/360°) × πr²
- πr² = 22/7 × 7² = 22/7 × 49 = 154
- = (90/360) × 154
- = (1/4) × 154 = 38.5
Worked example 2
A sector of a circle of radius 14 cm has area 77 cm². Find its centre angle.
(Use π = 22/7)
- Area = (θ/360°) × πr²
- πr² = 22/7 × 14² = 22/7 × 196 = 616
- 77 = (θ/360) × 616
- θ/360 = 77 ÷ 616 = 1/8
- θ = 360 ÷ 8 = 45
Where students go wrong
- Using 2πr (circumference) instead of πr² (area) inside the fraction.
- Forgetting the θ/360° fraction and giving the whole circle's area.
- Squaring the diameter instead of the radius.
- Answering in cm instead of cm².
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
How is the sector area different from the arc length formula?
Both use the fraction θ/360°, but sector area multiplies it by the whole area πr² and gives cm², while arc length multiplies it by the circumference 2πr and gives cm. If your answer for a sector comes out in cm you have used the wrong second factor.
Check the unit to catch the slip.
Can I find the sector area from the arc length?
Yes, indirectly. Use the arc length to find θ/360° first, then substitute that same fraction into (θ/360°) × πr².
Both formulas share the fraction, so once you know it from the arc, the area follows. Alternatively there is a neat relation: sector area equals half the arc length times the radius.
Is the sector formula on the SPM formula sheet?
Yes, (θ/360°) × πr² is printed, so you do not memorise it. You are marked on choosing πr² (not 2πr), reading θ in degrees, and squaring the radius.
Knowing it is given lets you spend your effort on clean substitution and correct square units instead of recalling it.