The area of a triangle

When "half base times height" isn't enough

• The familiar $\text{Area} = \tfrac{1}{2} \times \text{base} \times \text{height}$ needs the perpendicular height, which you often don't have.
• If instead you know two sides and the angle between them, use the trig area formula:

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

• $a$, $b$ — the two known sides.
• $C$ — the included angle, the one between those two sides.
• The $\sin C$ effectively supplies the missing height, so no perpendicular is needed.

Using the formula

• Identify the two sides and the angle wedged between them — the angle must be included, not opposite.
• Substitute and evaluate; area comes out in squared units.