Area of a Segment
What is the Area of a Segment?
A segment is created when a chord (a straight line across the circle) divides the circle into two parts. To find the area of a segment you need to find the area of the sector and subtract the area of the triangle.
It's easy to get confused between a sector and a segment. A nice way to remember is that a segment looks like an orange segment whereas a sector looks like a pizza slice.
Before you can calculate the area of a segment you need to be confident you can calculate the area of a sector and the area of a triangle.
To calculate the area of a segment, we will need to do three things:
First find the area of the sector
Next, find the area of the triangle in the sector
Finally subtract the area of the triangle from the area of the sector.
An Area of a Segment Example Question (Edexcel Higher November 2021, Paper 3, Question 7)
Example Question
The diagram shows a sector OPQR of a crcle, centre O and radius 8cm.
OPR is a triangle.
Work out the area of the shaded segment PQR.
Give your answer correct to 3 significant figures.
