Area of a Triangle

Exam code: 4024

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

Area of a Triangle

Area of a triangle

$Area = \frac{1}{2} a b \sin C$

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"!

Worked example

The following diagram shows triangle $ABC$ .

$AB = 32 cm$ , $AC = 1.1 m$ and angle $BAC = 74 °$ .

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, $Area = \frac{1}{2} a b \sin C$

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

$\begin{array}{rcl} Area & = & \frac{1}{2} (1.1) (0.32) \sin 74 \\ = & 0.16918 . . . \end{array}$

The area is 0.169 m² (to 3 s.f.)