Area of a Triangle (Cambridge International IGCSE Maths)

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

$\mathrm{Area}=\frac{1}{2}ab\mathrm{sin}C$

• C is the angle between sides $a$* *and $b$

• 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"!

Exam Hint You are given the triangle area rule on the formula sheet.

Worked Example The following diagram shows triangle $\mathrm{ABC}$.

$\mathrm{AB}=32\mathrm{cm}$, $\mathrm{AC}=1.1m$ and angle $\mathrm{BAC}=74^{\circ}$.

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

Answer:

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

Use the area of a triangle formula, $\mathrm{Area}=\frac{1}{2}ab\mathrm{sin}C$

You can either re-label the sides and angles to match the formula, or you can use the formula $\mathrm{Area}=\frac{1}{2}bc\mathrm{sin}A$ which is equivalent

$\begin{gathered} \text{Area} = 1 \frac{1}{2} ( 1.1 ) ( 0.32 ) \sin 74 \\ = 0.16918... \end{gathered}$

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