What is a crucial step in calculating the area of a triangle when proving its properties?

In calculating the area of a triangle, determining the length of the base is essential because the area formula for a triangle is given by ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ). To apply this formula effectively, one must first identify a base of the triangle, which is typically one of its sides. Once the base is established, the corresponding height must also be known, which is the perpendicular length from the opposite vertex to the base.

Without determining the length of the base, it is impossible to compute the area using this formula. While knowing the lengths of all three sides can provide further insight into the triangle's properties and can be used in Heron's formula for area computation, it is not the primary step for finding area in the more straightforward base-height method. Midpoints of segments and the sum of angles are not directly relevant for calculating the area. Thus, identifying the base is a crucial initial step in this process.