What is the formula for calculating the area of a triangle?

The formula for calculating the area of a triangle is most accurately represented by the formula A = 1/2 * base * height. The correct definition specifies that the area (A) is equal to one-half the product of the base of the triangle and its height.

In a triangle, the height is the perpendicular distance from the base to the opposite vertex, and the base is any one of the sides of the triangle that is chosen to be the base for the calculation. The division by two accounts for the triangular shape—it's essentially a portion of a rectangle that could be formed by extending the height from the base on both sides.

Other options reflect formulas for different shapes or concepts. The formula A = base • height implies the area of a rectangle or an incorrect representation of a triangle's area without considering the factor of one-half. The formula A = side • side might suggest area calculations for squares or rectangles but doesn't apply here as triangles do not have equal lengths for all sides. Lastly, A = length • width represents a rectangle, which relates to area but is not applicable to triangles specifically.

Understanding these distinctions allows one to choose the right formula based on the shape being analyzed, reinforcing the correct use of geometric principles in mathematical calculations.