The main way to find the area of a triangle is by using the formula:

Area=12×base×height\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}Area=21​×base×height

Here, the base is one side of the triangle, and the height is the perpendicular distance from that base to the opposite vertex. Other methods to find the area include:

• Heron's formula, when the lengths of all three sides (a, b, c) are known:

Area=s(s−a)(s−b)(s−c)\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}Area=s(s−a)(s−b)(s−c)​

where s=a+b+c2s=\frac{a+b+c}{2}s=2a+b+c​ is the semi-perimeter.

• Using two sides and the included angle θ\theta θ:

Area=12×side1×side2×sin⁡(θ)\text{Area}=\frac{1}{2}\times \text{side}_1\times \text{side}_2\times \sin(\theta)Area=21​×side1​×side2​×sin(θ)

• Special formulas for specific types of triangles like equilateral or isosceles.

In summary, the simplest and most common formula for the area is half the base times the height, but other formulas exist depending on what triangle measurements are available.