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

The formula for calculating the area of a triangle is indeed represented by one-half multiplied by the base and the height, often written as 1/2 x b x h. This formula arises from the geometric properties of triangles; specifically, the area of a triangle can be derived from the area of a rectangle.

When you consider a rectangle, its area is calculated by multiplying its length by its width. A triangle can be thought of as half of a rectangle when you draw an altitude from the top vertex to the base, effectively dividing the rectangle into two triangles. Therefore, by taking half of the product of the base (b) and the height (h), you can determine the area of the triangle.

The other options presented do not apply to finding the area of a triangle. The first option suggests multiplying the base by the height, which does not account for the fact that a triangle is only half of that rectangle. The choice referring to length multiplied by width is the area formula for a rectangle, not a triangle. Lastly, the expression involving 3 times the sum of base and height does not relate to any standard formula for calculating the area and does not accurately represent the geometric relationship within a triangle.