The area of a triangle can be calculated using the formula A = 1/2 a*b*sin(theta), where a and b are the lengths of two sides and theta is the included angle. To derive this formula, one can start with the standard area formula A = 1/2 b*h and relate the height to the sine of the angle. By dropping a perpendicular height from the vertex opposite side a, the height can be expressed as h = b*sin(theta). It is important to remember that the triangle in question is not necessarily a right triangle, which affects how the height is determined. Understanding these relationships allows for the correct application of the area formula for any triangle.
