National 5 Maths
Area of a Triangle
Course content
- Calculate the area of a triangle using the trigonometric formula:
Textbook page references
- Zeta National 5+ Maths pp.224-225
- TeeJay Maths Book N5 pp.73-75
- Leckie National 5 Maths pp.293-298
Key ideas
- This formula works in any triangle: right-angled or non-right angled.
- This formula only needs us to know two the lengths of two sides and the angle enclosed between them.
- Unlike the other formula for the area of a triangle, \(A\!\,=\!\,\frac{1}{2}bh \), we don't need to know the vertical height.
N5 Maths revision course
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Example 1 (calculator)
In the triangle below, BC = 9 mm, AC = 15 mm and angle C = 60°.
Calculate the area of triangle ABC.
Example 2 (non-calculator)
In the triangle below, AB = 5 cm, BC = 3 cm and sin B = \( \frac{1}{\sqrt{2}} \).
Calculate the area of triangle ABC, expressing your answer as a fully simplified surd with a rational denominator.
Recommended student book
Zeta Maths: National 5 Maths TextbookBest price, direct from the publisher
Example 3 (calculator)
Calculate the area of an equilateral triangle with side lengths of 5 cm.
Example 4 (calculator)
Calculate the area of a regular hexagon with side length 10 cm, giving your answer correct to 3 significant figures.
Example 5 (calculator)
A triangle of area 50 cm2 has two sides with lengths 12 cm and 10 cm. The angle between these two sides is acute. Calculate this angle.
Recommended revision guides
How to Pass National 5 MathsBrightRED N5 Maths Study Guide
Example 6 (calculator)
A triangle of area 50 cm2 has two sides with lengths 12 cm and 10 cm. The angle between these two sides is obtuse. Calculate this angle.
Example 7 (calculator)
SQA National 5 Maths 2015 P2 Q11
The top of a table is in the shape of a regular hexagon. The three diagonals of the hexagon which are shown as dotted lines in the diagram below each have length 40 centimetres.
Calculate the area of the top of the table.
Example 8 (non-calculator)
SQA National 5 Maths 2017 P1 Q7
In triangle DEF:
• DE = 8 centimetres
• EF = 12 centimetres
• sin E \(=\frac{2}{3}\)
Calculate the area of triangle DEF.
N5 Maths practice papers
Non-calculator papers and solutionsCalculator papers and solutions
Example 9 (calculator)
SQA National 5 Maths 2019 P2 Q3
The diagram shows triangle PQR.
• PR = 45 centimetres
• PQ = 70 centimetres
• Angle QPR = 129°
Calculate the area of triangle PQR.
Example 10 (calculator)
SQA National 5 Maths 2023 P2 Q15
In the diagram:
• AC is perpendicular to BC
• AB = 18 centimetres
• BD = 6 centimetres
• BC = 8 centimetres.
The area of triangle ADE is 160 square centimetres.
Calculate the length of AE.
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Past paper questions
• All past paper questions by topic |
• 2014 Paper 2 Q13 (with sector area) • 2015 Paper 2 Q11 (hexagon) • 2017 Paper 1 Q7 • 2018 Paper 2 Q17 (with sector area) • 2019 Paper 2 Q3 • 2021 Paper 2 Q8 (with sector area) • 2022 Paper 2 Q6 • 2023 Paper 2 Q15 (finding a length) |
Other great resources
Videos - Maths180.com |
Video - Tynecastle HS |
Video - Mr Graham Maths |
Videos - YouKenMaths 1. Area of a triangle 2. Hexagon, decagon etc |
PowerPoint - MathsRevision.com |
Notes and videos - Mistercorzi |
• Revision notes - BBC Bitesize • Test yourself - BBC Bitesize |
Notes - Maths4Scotland.co.uk |
Theory guide - National 5 Maths |
Worked examples - Maths Mutt |
Lesson notes - Maths 777 |
Notes - D R Turnbull |
Exercises - Larkhall Academy Pages 10-11 Ex 7 |
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