Question

What is the area of the quadrilateral bounded by `y=5`; `x=1`; `y=1`; and `y=-2x+9`?

Answer 1

`8` square units

Explanation:

Note that `y=-2x+9` can be written as `x=(9-y)/2`
making it easier to evaluate the intersection coordinates for
`y=-2x+9` and `y=5`
`color(white)(y=-2x+9)` and `y=1`

From the above diagram it is clear that the area is

`color(white)("XXX")color(blue)4 xx (color(blue)1 + color(blue)3)/2`

`color(white)("XXX")=8`