Finding the Area Between Lines and Axes

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

To find 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

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