GCSEMathsEdexcelHigherRevision Notes4. Geometry & MeasuresSine, Cosine Rule & Area of TrianglesArea of a Triangle

Area of a Triangle (Edexcel GCSE Maths)

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Written by: Amber

Reviewed by: Dan Finlay

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Area of a Triangle

How do I find the area of a non right-angled triangle?

  • The area of any triangle can be found using the formula

Area space equals space 1 half a b space sin space C

  • C is the angle between sides a and b

Non Right-Angled Triangle labelled with angles A, B and C and opposite corresponding sides a, b and c.

  • Label your triangle correctly

    • Make sure that C is always the angle between the two sides

  • If angle C is 90°, you get a right-angled triangle

    • sin 90° = 1 so the formula becomes the familiar "Area = ½ × base × height"!

 

Examiner Tips and Tricks

  • You are given the triangle area rule on the formula sheet

Worked Example

The following diagram shows triangle ABC.

AB space equals space 32 space cm, AC space equals space 1.1 space straight m and angle BAC space equals space 74 degree. 

Triangle ABC, whereAB = 32 cm, AC = 1.1 m and angle BAC = 74º.

Calculate the area of triangle, giving your answer in m2.

Label the sides of the triangle
Convert the sides to be in the same units

Triangle ABC with sides opposite angles labelled with the corresponding lowercase letters. Side AB units converted from 32 cm to 0.32 m.

Use the area of a triangle formula, Area equals 1 half b c space sin space A

table row Area equals cell 1 half open parentheses 1.1 close parentheses open parentheses 0.32 close parentheses space sin space 74 end cell row blank equals cell 0.16918... end cell end table

The area is 0.169 m2 (to 3 s.f.)

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    Author
    Reviewer
    Amber

    Author: Amber

    Expertise: Maths

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.