A triangle is a geometric shape that consists of three sides and three vertices located where one side meets another. All triangles have a sum of internal angles of 180 degrees. There are three classifications of triangles determined by the lengths of their sides: equilateral triangles, isosceles triangles and scalene triangles. A scalene triangle is an irregular triangle with no equal sides or internal angles. There are many methods of finding the area of a scalene triangle, but the most common methods include the "half base times height" method, the "side-angle-side" method and the Heron's formula method. A method is chosen based on the information you know about the triangle.

### Half Base Times Height Method

Use the "half base times height" method if the base and height of the scalene triangle are known.

Multiply the length of the base of the triangle by the height of the triangle.

Divide the result by 2 to obtain the area of the scalene triangle.

### Side-Side-Angle Method

Use the "side-angle-side" method if two sides and the included angle are known. An included angle is the angle that is "sandwiched" between two rays.

Multiply the lengths of the two known legs together then multiply the result by the sine of the included angle.

Divide the result by 2 to obtain the area of the scalene triangle.

### Heron's Formula Method

Use Heron's Formula if all three sides of the scalene triangle are known.

Find half of the perimeter "p" of the triangle by adding the three sides together then dividing the result by 2.

Subtract each of the values of the side length from "p." Then multiply the results together. For example, if the side lengths of a scalene triangle are "a," "b," and "c" and the half perimeter is "p," the expression becomes: (p - a) * (p - b) * (p - c).

Multiple the result of the previous expression by the value of "p."

Take the square root of the result to obtain the area of the scalene triangle.