Finding the Area Between Lines and Axes

The graph is of the line(1). We have to find the area of the region A, which is a triangle. Towards this end, we find the base and the height of the triangle.

To fin d the base, note that at the point where the line crosses the– axis,Substitute this value ofinto (1):

To fin d the height, note that at the point where the line crosses the– axis,Substitute this value ofinto (1):

The base is 8 and the height is 4 so the area is

To find the height of the triangle now we have to solve the simultaneous equations

(1)

(2)

(2)-(1) gives

Subinto (1) to give

To find the base we have to find where the lines cross the– axis. This will be where y=0.

The base of the triangle is 12—8=20 and the area is