



 
Cliff, No, you do not have enough information. If you make one of the edges next to the known one a few feet long and the fourth edge parallel to the known one, the area will be only a few hundred square feet. Now swing the edge around so it's nearly parallel to the opposite edge; the new area is huge. Somewhere in between you would have had the right area and satisfied all your conditions. But (apart from being fairly short) the length you picked was arbitrary. Good Hunting! Cliff wrote back
Hello Cliff,
We would like an equation for the area of this figure, and for it to only involve the variable, x, the distance between the two parallel sides. Let’s add some extra perpendicular lines, and some variables. From our new picture, we have the following equation for the area of this entire figure:
We can eliminate the extra variables using some knowledge of trigonometry:
Which means that, y = x/tan 65^{o} and z = x tan 50^{o}. Substituting these into our area equation, and setting area to 130,680 square feet we get: After simplification, you can solve the resulting quadratic equation for x. Tyler
 


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