Which formula represents the area of a triangle?

The area of a triangle is calculated using the formula ( \frac{1}{2} \times \text{base} \times \text{height} ). This formula is derived from the understanding that a triangle can be thought of as half of a rectangle or a parallelogram.

When you multiply the base by the height, you find the area of a rectangle that would encompass the triangle. Since a triangle occupies half of that rectangle's area, you take half of the product of the base and height to get the area of the triangle. Therefore, the correct formula accurately reflects this relationship.

The other options do not correctly calculate the area of a triangle. Simply multiplying the base by the height would give you the area of a rectangle, while adding or subtracting the height from the base does not conform to the geometric principles used to determine area. Thus, ( \frac{1}{2} \times \text{base} \times \text{height} ) is the only formula that accurately represents the area of a triangle.