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

The formula for calculating the area of a triangle is derived from the basic definition of area, which is generally related to the dimensions of the shape involved. For a triangle, the area can be understood as half the product of its base and height.

The reason this formula is 1/2 × Base × Height is that a triangle can be visualized as half of a rectangle. When you multiply the base by the height, you get the area of a rectangle that encompasses the triangle. Since a triangle occupies half that space, the area is therefore halved, resulting in the formula of 1/2 × Base × Height.

This principle applies to any triangle, regardless of its type (scalene, isosceles, or equilateral) as long as you have the measurements for the base and the height. The height must be measured as the perpendicular distance from the base to the opposite vertex.

In contrast, other options do not accurately reflect the relationship between the dimensions of a triangle. For instance, simply multiplying the base by the height does not account for the triangular shape, which leads to an overestimation of the area. Adding the base and height ignores the necessary dimensional relationship altogether, while dividing the base by the height