To find the area of a triangle, the most common and straightforward formula is:

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

Here, the base is any one side of the triangle, and the height (or altitude) is the perpendicular distance from the chosen base to the opposite vertex. The base and height must be perpendicular to each other. The area is measured in square units, such as square centimeters (cm²) or square meters (m²)

Steps to Use This Formula:

1. Identify the base of the triangle.
2. Measure or find the height perpendicular to this base.
3. Multiply the base by the height.
4. Divide the result by 2.

Example:

If a triangle has a base of 3 cm and a height of 4 cm, the area is:

Area=12×3×4=6 cm2\text{Area}=\frac{1}{2}\times 3\times 4=6\text{ cm}^2Area=21​×3×4=6 cm2

Other Methods to Find Area:

• Heron's Formula: When all three sides aaa, bbb, and ccc are known, first calculate the semi-perimeter s=a+b+c2s=\frac{a+b+c}{2}s=2a+b+c​, then the area is:

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)​

• Using Two Sides and Included Angle: If two sides and the angle between them are known, use:

Area=12×a×b×sin⁡(C)\text{Area}=\frac{1}{2}\times a\times b\times \sin(C)Area=21​×a×b×sin(C)

where aaa and bbb are the sides and CCC is the included angle

. These formulas cover all types of triangles—scalene, isosceles, equilateral, and right-angled triangles