Area Rule

Study Notes

The area rule helps calculate the area of a triangle that is not right-angled using the sine ratio. It involves using the sine of the angle included between two sides of the triangle.

• Area Rule — the area of any triangle is equal to half the product of the lengths of two sides multiplied by the sine of the included angle. Example: For a triangle with sides a and b, and included angle C, the area is $\frac{1}{2}ab \sin C$.

Exam Tips

Key Definitions to Remember

• The area of a triangle is $\frac{1}{2}ab \sin C$, where a and b are sides and C is the included angle.

Common Confusions

• Confusing the area rule with the sine rule for finding sides and angles.
• Forgetting to use the sine of the included angle.

Typical Exam Questions

• How do you find the area of a triangle with sides 5 cm and 7 cm and an included angle of 60 degrees? Use the formula $\frac{1}{2}ab \sin C$ to find the area.
• What is the area of a triangle with sides 8 cm and 10 cm and an included angle of 45 degrees? Calculate using $\frac{1}{2}ab \sin C$.
• How can you find the area of a parallelogram using the area rule? Use the area rule for triangles and apply it to the two triangles forming the parallelogram.

What Examiners Usually Test

• Application of the area rule to find the area of non right-angled triangles.
• Understanding of when to use the sine of the included angle in calculations.