What is the area of the triangle if the vertices are (0,2), (0, 0), (3, 0)?

The correct option is 3 sq. unit.

To find the area of the triangle with the given vertices, we can analyze the coordinates of the points:
Let the vertices be:
$P_1=(0,2)$
$P_2=(0,0)$
$P_3=(3,0)$

Notice that two of the vertices lie along the coordinate axes:
- The vertex $P_2(0,0)$ is at the origin.
- The vertex $P_1(0,2)$ lies on the y-axis, representing a vertical height.
- The vertex $P_3(3,0)$ lies on the x-axis, representing a horizontal base.

Since the x-axis and y-axis are perpendicular, this forms a right-angled triangle where:
- The base is the distance along the x-axis from $(0,0)$ to $(3,0)$, which is $3$ units.
- The height is the distance along the y-axis from $(0,0)$ to $(0,2)$, which is $2$ units.

The standard formula for the area of a triangle is:
$\text{Area}=\frac{1}{2}\times \text{base}\times \text{height}$

Substituting the base and height values into the formula:
$\text{Area}=\frac{1}{2}\times 3\times 2$
$\text{Area}=3\text{ sq. unit}$

Thus, the area of the triangle is indeed 3 sq. unit.