What formula represents the area of a triangle?

The formula that represents the area of a triangle is ( \frac{1}{2} b \times h ). In this equation, ( b ) stands for the base of the triangle, and ( h ) represents the height. The concept behind this formula is rooted in the geometrical understanding that the area of a triangle can be derived from the area of a rectangle. If you visualize a triangle situated within a rectangle, the area of the rectangle is calculated as the base times the height. The triangle, being half of the rectangle when both share the same base and height, thus has half the area of that rectangle, leading to the formula of ( \frac{1}{2} ) times the base times the height.

In contrast, the other candidates represent different geometrical concepts. The formula combining ( b_1 + b_2 ) divided by 2 times ( h ) is used specifically for calculating the area of a trapezoid, not a triangle. The formula ( b \times h ) provides the area of a rectangle or parallelogram, while ( \pi r^2 ) calculates the area of a circle, emphasizing that each formula is tailored for distinct shapes.