Home   >  Worksheets   >  GCSE questions by topic   >  Area of a segment

MathsLinks Logo Questions by topic

Last update: 05/11/2026

Give feedback : Buy me a coffee

Area of a segment

Free Printable Area of a segment PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 7)

Download free area of a segment worksheets (PDF), GCSE maths past paper questions and worked solutions for Area of a segment (7U). This is a Grade 7 geometry topic from the GCSE questions by topic collection for Higher tier GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Corbett Maths, Maths Made Easy, M4ths.com, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our area of a segment revision notes and worked examples with diagrams, try real GCSE past paper area of a segment questions with step-by-step solutions, or download a PDF of all area of a segment worksheet links.

Free Area of a segment PDF Worksheets & Answers

Grade 7 • Topic 7U
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Practice Questions & answers
 Qs Ans
Textbook Exercise & answers
 Qs Ans
MME worksheet & model answers
 Qs Ans
GCSE worksheet & answers
 Qs -
GCSE topic booklet & answers
 Qs Ans
PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
 Qs Ans
PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Grade 7 topics
7A - Surds7B - Bounds
7C - Proportion (harder)7D - Algebraic fractions
7E - The quadratic formula7F - Factorising harder quadratics
7G - Trigonometric & exp. Graphs7H - Rearranging (harder)
7J - Functions (harder)7K - Iteration
7L - Area of any triangle7M - The sine rule
7N - The cosine rule7P - Congruent triangles
7Q - 3D pythagoras / trig.7R - Histograms
7S - Conditional probability7T - Exact trig. values (harder)
7U - Area of a segment
GCSE Maths Grade 7 Revision Notes & Method

Guide to Area of a segment: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

A segment is the region enclosed between a chord and an arc of a circle. To find the area of a minor segment with radius r and central angle θ, subtract the area of the isosceles triangle formed by the two radii and the chord from the area of the sector:

Area of segment = Area of sector − Area of triangle = (θ360 × πr2) − (12r2 sin θ). To find the perimeter of a segment, add the arc length (θ360 × 2πr) to the chord length (found using the Cosine Rule).

Example 1: Find the area of the minor segment of a circle with radius 10 cm and central angle 72° (3 s.f.).

O 72° 10 cm 10 cm Minor segment

Solution:

Area of sector = 72360 × π × 102 = 20π = 62.8318... cm2
Area of triangle = 12 × 102 × sin 72° = 47.5528... cm2
Segment area = 62.8318... − 47.5528... = 15.2790...
Answer: 15.3 cm2 (3 s.f.)

Example 2: Find the exact area of a minor segment with radius 6 cm and central angle 60°.

Solution:

Area of sector = 60360 × π × 62 = 6π cm2
Area of triangle = 12 × 62 × sin 60° = 18 × √32 = 9√3 cm2
Subtract triangle from sector:
Answer: (6π − 9√3) cm2
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Area of a segment Questions & Answers

Past Paper Example 1 IGCSE Jan 2023 1H Q21 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows the cross section of a circular water pipe.
72°4.8 cmOABCDiagram NOTaccurately drawn
OABC is a sector of the circle, centre O
The shaded region in the diagram represents the water flowing in the pipe.
The water flows at 14 cm/s in the pipe.
Work out the volume of water that has flowed through the pipe in 3 minutes.
Give your answer in cm3 correct to 3 significant figures.
Worked Solution & Mark Scheme (5 marks)
Area of sector OABC = (72/360) × π × 4.8² = 14.47645... cm² M1
Area of triangle OAC = ½ × 4.8² × sin 72° = 10.95617... cm² M1
Area of shaded segment = 14.47645... − 10.95617... = 3.52028... cm² M1
In 3 minutes (180 seconds), length of flow = 14 × 180 = 2520 cm M1
Volume = 3.52028... × 2520 = 8871.1... ≈ 8870 cm³ (3 s.f.). A1
Answer: 8870 cm³
Past Paper Example 2 GCSE Nov 2021 3F Q27 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a sector OPQR of a circle, centre O and radius 8 cm.
OPRQ8 cm8 cm
OPR is a triangle.
Work out the area of the shaded segment PQR.
Give your answer correct to 3 significant figures.
Worked Solution & Mark Scheme (4 marks)
(The area of a triangle is ½ × base × height)
Area of sector = ¼ × π × 8² = 16π ≈ 50.265 cm² M2
Area of triangle OPR = ½ × 8 × 8 = 32 cm² M1
Segment = 50.265 – 32 = 18.3 cm² (3 s.f.) A1
Answer: 18.3 cm²
Past Paper Example 3 Specimen Set 2 2H Q7 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
ABCO4.8 cm
The arc ABC is a quarter of a circle with centre O and radius 4.8 cm.
AC is a chord of the circle.
Work out the area of the shaded segment.
Give your answer correct to 3 significant figures.
The arc ABC is a quarter of a circle with centre O and radius 4.8 cm.
AC is a chord of the circle.
Work out the area of the shaded segment.
Give your answer correct to 3 significant figures.
Worked Solution & Mark Scheme (3 marks)
(The area of a circle is πr²)
Area of quarter circle = ¼ × π × 4.8² = 5.76π ≈ 18.0956 cm² M1
Area of triangle OAC = ½ × 4.8 × 4.8 = 11.52 cm² M1
Shaded segment = 18.0956 – 11.52 = 6.58 cm² (3 s.f.). A1
Answer: 6.58 cm²

← 7T Exact trig. values (harder)

Back to GCSE questions by topic

8A Quad. sim. equations →