I’ll preface this by saying that this is *not* a homework problem. It’s more or less a geometry problem that I’m attempting to solve for a relative of mine regarding acreage.

## There’s a plot of land with the following dimensions: 494.5’ x 105’ x 438.71’ x 105’. The shape is roughly like this (slope of bottom side greatly exaggerated):

‘’’’’’’’’’

‘’’’’’’’’’

‘’’’’’’’’/

‘’’’’’/

‘’’/

/

Based on some other dimensions I’ve been able to determine functions that model each side, assuming the origin is placed at the top left. The top side is simply y=0 from x=0 to 105.6. The left side is y=(-0.155)*x from x =0 to 75.743. The bottom side is y=(0.568)*x - 531.69 from x=75.74 to 172.798. The right side is y=(-0.155)*x-16.368 from x=1-5.6 to 172.798.

Clearly, there are several ways I could solve this. Since the top and bottom are nearly equal, I could approximate the shape with a trapezoid and find the area that way. I could also divide this into many triangles and solve it that way. However, one of my quirks is that I get fixated on solving a problem a particular way and refuse to be satisfied with an answer obtained any other way. I’d like to solve this with integral calculus. If the left and right curves weren’t parallel (i.e. they intersected at a point), I could find the area between them easily. But the fact that they’re parallel and one of the bounding curves is not constant is throwing me quite a roadblock. Frankly, I’m embarrassed to admit I can’t solve this with calculus.

Any tips?