Where can I download free surface area PDF worksheets with answers?

On this MathsLinks page you can download free printable surface area PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Ken Stafford (1), Maths Genie, Corbett Practice, Corbett Textbook, plus a printable one-page surface area revision guide.

What GCSE grade is surface area (4N)?

Surface area (topic code 4N) is a Grade 4 geometry topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Surface area Worksheets (PDF) with Answers — GCSE Maths

Free Surface area PDF Worksheets & Answers

Grade 4 • Topic 4N

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (1) Practice worksheet & worked solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
Dr Austin (1) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (2) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (3) Practice grid / worksheet & answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
E Classroom 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
esheets Self-marking online worksheet	Page

Grade 4 topics
4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction

Explanation:

The total surface area of a 3D solid is the sum of the areas of all its outer faces, measured in square units (cm² or m²). A cuboid has 6 rectangular faces in 3 identical opposite pairs: Surface Area = 2(lw + lh + wh).

For a triangular prism, add the areas of the 2 triangular ends (12 × base × height each) and the 3 rectangular sides. Be careful not to confuse the slant edge of the triangle with its perpendicular height!

Example 1: Find the total surface area of a cuboid measuring 8 cm by 5 cm by 3 cm.

2(8×5) = 80

2(8×3) = 48

2(5×3) = 30

Total = 158 cm²

Example 2: A right-angled triangular prism has ends 3 cm, 4 cm, 5 cm and length 10 cm. Find its total surface area.

2 ends = 2(12×3×4) = 12

3 sides = 30+40+50 = 120

Total = 132 cm²

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Surface area Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 AQA Nov 2022 2H Q8 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

(a) The total length of all edges of the cuboid is 80 cm and volume > 200 cm³. Work out one possible set of whole number values for w, x and y. [2 marks]
8 (b) Circle the expression for the total surface area of a cube of side 3a cm. [1 mark]

(a) Here is a cuboid.
w, x and y are **different** whole numbers. [2 marks]

The total length of **all** the edges of the cuboid is 80 cm
The volume is **greater** than 200 cm³
Work out one possible set of values for w, x and y.

(b) Here is a solid cube. [1 mark]

Circle the expression for the **total** surface area in cm²
36a 54a 36a² 54a²

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

(The volume of a cuboid is length × width × height)
4(w + x + y) = 80 ⇒ w + x + y = 20 M1
Try 8, 7, 5: 8 + 7 + 5 = 20 and 8 × 7 × 5 = 280 > 200 A1

Answer (a): w = 8, x = 7, y = 5

Part (b) Solution:

(The area of a circle is πr²)
Area of one face = (3a)² = 9a²
Total surface area = 6 × 9a² = 54a² B1

Answer (b): 54a²

Past Paper Example 2 IGCSE Nov 2024 2F Q22 / 2H Q6 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

The diagram shows a solid triangular prism.

Work out the total surface area of the triangular prism.

Worked Solution & Mark Scheme (3 marks)

Two triangular ends = 2 × (½ × 8 × 6) = 48 cm² M1
Three rectangular faces = (15 × 8) + (15 × 6) + (15 × 10) = 120 + 90 + 150 = 360 cm² M1
Total = 48 + 360 = 408 cm² A1

Answer: 408 cm²

Past Paper Example 3 AQA Jun 2023 3F Q19 / 3H Q6 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

Here is cuboid A.
Cuboid B is made from **two** of cuboid A.

volume of A : volume of B = 1 : 2
Matthew says,
“surface area of A : surface area of B must be 1 : 2 because B is made of 2 of A.”
Is Matthew correct?
Tick **one** box.
[ ] Yes [ ] No [ ] Cannot tell
Give a reason for your answer.

Worked Solution & Mark Scheme (2 marks)

(The volume of a cuboid is length × width × height)
When two cuboids are joined together, two touching faces are hidden inside, so the surface area of B is less than twice the surface area of A. M1 C1

Answer: No — two faces are joined inside B so they are not part of the outer surface area (e.g. 6 faces vs 10 faces)

← 4M Angles in polygons

Back to GCSE questions by topic

4P Volume of a cuboid →

Surface area

Free Surface area PDF Worksheets & Answers

Guide to Surface area: Explanation, Diagrams & Worked Examples

GCSE Past Paper Surface area Questions & Answers