Area inside 4 tangents

jahaddow

1. The problem statement, all variables and given/known data
Ok, I have a cubic function, y=(x-6)(x-1)(x-9) or y = x³-16x²+69x-54
I then have four tangents to make a quadrilateral, the tangents are as follows.
y=7.75x+14.75
y=-6.25x+56.25
y=7.75x + -76.231
y=-6.25x + 31.602
I need to find the area inside the tangents, except I have no idea where to start, Thankyou for any help in advance.

rock.freak667

Start by sketching the lines. What do you notice about these pairs of lines:

y=7.75x+14.75 & y=7.75x + -76.231

y=-6.25x+56.25 & y=-6.25x + 31.602

What sort of quadrilateral figure is formed?

jahaddow

A Parallelogram, But I dont see how I can get the area from the equations?

rock.freak667

You can find where the lines intersect one another and thus find the coordinates of the corners. You can then find the lengths of the lines. Split the area into two triangles and find the areas.

jahaddow

So, How do I do that?

rock.freak667

Solve each pair of equations to get the points of intersection. Find the lengths of the lines and then find the area of the shape.

Or you could split the area into two triangles and calculate it.