The surface is  and the vertices of the triangle are .

Volume of the solid :

The volume of the solid V under the surface  and lies above the region  then .

Graph :

(1) Draw the coordinate plane.

(2) Plot the vertices .

(3) Connect the plotted vertices with a smooth triangle.

Observe the graph :

The limits of y are varying from 1 to 2 , so .

Find the bounds for x :

Consider the points .

From the points, coordinates are equal then the equation of the line parallel to axis.

So the equation of the line is 

Consider the points .

Using two points form of a line equation is .

Substitute  in the line equation.

Therefore  then .

Find the volume of the solid.

The obtained region is .

Then 

The volume of the solid is .