What is the area formula for a triangle?

The area formula for a triangle is derived from the fundamental definition of area in geometry. The formula, which is (Base x Height) / 2, captures the relationship between the base of the triangle and its height, which is the perpendicular distance from the base to the opposite vertex.

To understand this more clearly, consider a rectangle with a base and a height. The area of the rectangle is given by Length x Width. A triangle can be viewed as half of a rectangle when you draw a diagonal from one corner to the opposite corner. Therefore, because a triangle occupies half of the area of that rectangle, the area is calculated by taking the base multiplied by the height and dividing by two.

This formula is applicable to all types of triangles, whether they're equilateral, isosceles, or scalene, as long as you correctly identify the base and the corresponding height. Other options provided do not represent the area of a triangle, which further reinforces the correctness of this formula.