A Level Maths Notes: C1 – 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 find the base, note
that at the point where the line crosses the
–
axis,
Substitute
this value of
into
(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
Sub
into
(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