Sheet № 154 · Foundation + Higher · AQA · Edexcel · OCR
Sector Area –
Sector area is a common GCSE Maths topic tested across AQA, Edexcel, and OCR on both Foundation and Higher papers. A sector is a "slice" of a circle, like a pizza slice, and its area depends on the radius and the angle at the centre. This guide covers the area formula, perimeter of a sector, and how to handle reverse problems where you fi
§Key definitions
Question:
Find the area of a sector with radius 6 cm and angle 90°. Give your answer to 1 decimal place.
Answer:
Area = 28.3 cm² (1 d.p.)
Q1 (Foundation):
Find the area of a sector with radius 7 cm and angle 60°. Give your answer to 1 d.p.
Q2 (Foundation):
A semicircular sector has a diameter of 20 cm. Find its area in terms of π.
Q3 (Higher):
A sector has an area of 75 cm² and a radius of 10 cm. Find the angle at the centre to 1 d.p.
§Formulas to memorise
Area of a sector = (θ / 360) × πr²
Perimeter of a sector = 2r + arc length = 2r + (θ / 360) × 2πr
Area of a full circle = πr²
Identify the radius — (r) and the angle at the centre (θ).
Write the formula: — Area = (θ / 360) × πr².
Substitute — the values and calculate.
For the perimeter — , add the arc length to twice the radius (the two straight edges).
Round — to the required accuracy or leave in terms of π.
Worked example
Find the area of a sector with radius 6 cm and angle 90°. Give your answer to 1 decimal place.
Working:
⚠ Common mistakes
- ✗Confusing arc length and sector area formulas. Arc length uses 2πr (circumference); sector area uses πr² (area). Make sure you pick the right one.
- ✗Forgetting the two radii in the perimeter. The perimeter of a sector includes the arc and the two straight edges (radii), so you add 2r to the arc length.
- ✗Squaring the diameter instead of the radius. If the question gives the diameter, halve it before squaring.
✦ Exam tips
- →When asked for perimeter of a sector, many students only calculate the arc length and forget the two radii. Always add 2r.
- →Show your substitution into the formula clearly — this earns method marks.
- →If the question says "in terms of π", simplify the numerical coefficient and leave π in your answer.
- →Sector area and arc length often appear together. Read the question carefully to determine which one is asked for.