GCSE Maths Revision Guide
Area & Arc of Sectors
Calculating arc lengths and sector areas of circles. This free GCSE Maths module combines short explanations, worked examples, flashcard-style recall, and timed practice so students can revise the topic without creating an account.
Foundation Skills
Fractions of a Circle
If the angle is 90°, it is 90/360 or 1/4 of the circle. Calculate the full circle area, then multiply by the fraction.
Example: Full area 40, angle 90° → Sector area = 10.
Semicircles & Quadrants
A semicircle is half a circle (180°). A quadrant is a quarter (90°).
Perimeter of a Sector
The total boundary: arc length + TWO radii. Don't forget the straight edges!
Example: Arc 10cm, Radius 5cm → Perimeter = 20cm.
Higher Skills
Arc Length Formula
Formula: L = (θ / 360) × π × d
Sector Area Formula
Formula: A = (θ / 360) × π × r²
Example: r=6, θ=60°: (60/360) × 36π = 6π ≈ 18.8 cm²
Segments (Tricky!)
Area of segment = Area of sector − Area of triangle.
Working Backwards
Given the sector area and radius, find the angle by rearranging the formula.
Example: θ = (Area × 360) / (πr²)