Area of triangle whose two vertices formed from the x-axis and line y = 3 – |x| is,

The correct option is "None of these".

Step-by-step Explanation:

1. Identify the given information:
The question refers to a triangle where two of its vertices are formed by the intersection of the line
$y=3-\left|x\right|$
and the x-axis.

2. Find the coordinates of these two vertices:
The equation of the x-axis is
$y=0$
. Substituting
$y=0$
into the equation of the line, we get:

$$3-\left|x\right|=0$$

$$\left|x\right|=3$$

$$x=\pm 3$$

3. Analyze the requirements of a triangle:
A triangle is a two-dimensional geometric shape that is uniquely defined by three non-collinear vertices. Knowing only two vertices allows us to define a line segment (the base of the triangle), but does not specify the height or the position of the third vertex.

4. Conclusion:
Since the third vertex of the triangle is not specified or defined in the question, the triangle's shape and area cannot be determined. Consequently, the correct choice is "None of these".