What is the formula for the area of a triangle?

The formula for the area of a triangle is derived from the concept of finding the area of a rectangle. When you think about a triangle, it can be visualized as half of a rectangle when divided by the diagonal that runs from one corner to the opposite side.

To calculate the area of a triangle, you take the base of the triangle and the height, which is the perpendicular distance from the base to the opposite vertex. The formula is structured as ( A = \frac{1}{2} \times \text{base} \times \text{height} ). This factor of one-half accounts for the fact that a triangle occupies half the area of a rectangle with the same base and height.

Thus, the correct choice encapsulates this relationship by ensuring that the area reflects the true size of a triangle. The other options either misinterpret the formula or fail to incorporate the necessary factor to scale the area appropriately, leading to irrelevant or incorrect representations of a triangle's area.