What is the formula for the area of a triangle?

The area of a triangle is given by the formula: area = 1/2 * base * height. This formula is derived from the fact that a triangle can be viewed as half of a rectangle. To understand this, consider a rectangle that has the same base and height as the triangle. The area of the rectangle is calculated as base multiplied by height. Since a triangle only occupies half of this rectangle, the area is effectively half of that value, leading to the formula for the area of a triangle being one-half of the base multiplied by the height.

This concept is fundamental in geometry and is essential for solving a variety of problems related to triangles. The other options presented do not accurately reflect the relationship between the dimensions of a triangle and its area, as they either omit the necessary factor of one-half or mistakenly combine the base and height in a way that does not represent area.