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Expert: - 10/23/2008


Question

figure v
Tim.
I chose (b) for the answer. If it is wrong can you please provide the correct answer with explanation. I would be grateful.please see attached jpeg,

1- the trapezoid in figure V has equal non parallel sides.The upper base is 6, the lower base is 16, and the diagonal is 12.what is the altitude of the trapezoid?

Answer
I'll assume there are equal angles in this trapezoid at the base and at the top (at least that's the way the picture looks).  This means that both of the sides are of equal length.  If there are not, the area would be unknown since we do not know what angle the line is at.  It could be at a large or a small angle with the bottom.

Construct a triangle going from the top right (where the top, right side, and angle all intersect that goes straight down and interesects the bottom at right angles.

The length of the base of the triangle on the right side can be found.  It is the length of the base of the trapezoid minus 1/2 the difference between the top length and the bottom length { (16-6)/2 = 5 }.  Therefore, the length of the other base { on the left of the verticle line | is 16 - 5 = 11.

If the base is 11 and the diagonal is 16, the other side is
√(16²-11²).

To find the area, take this value times the sum of the lengths of the top and bottom all over two to get the answer.  It would be
(6+16) * √(16²-11²) / 2.

Scott A Wilson

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