The reason why 0.5 is used in the formula for the area of a triangle is because a triangle can be thought of as half of a rectangle.

When you calculate the area of a rectangle, you multiply the length by the width. However, in the case of a triangle, the base is equivalent to the length of the rectangle, but the height is only half of the width.

So, to account for the fact that a triangle is half of a rectangle, we multiply the base by the height and then divide the result by 2. This is why the formula for the area of a triangle is given as 0.5 × base × height.