What is the area formula for a triangle?

The area formula for a triangle is derived from the relationship between the triangle and a rectangle. The basic idea is that a triangle occupies half the area of a rectangle with the same base and height.

To understand why the correct formula is (1/2) × base × height, consider that if you have a rectangle, its area is calculated by multiplying the length of the base by the height. Since a triangle is essentially half of that rectangle when divided along one of its diagonals, the area of the triangle is therefore half of that area.

By using the formula, you multiply the length of the base by the height to find the same rectangular area first and then divide that product by 2 to get the area of the triangle. Thus, this formula effectively captures the geometric properties of triangles and ensures accurate area calculations.