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September 18, 2014

September 18, 2014

Posted by **Pre Calc** on Monday, October 5, 2009 at 1:43pm.

The parallel sides of a trapezoid are 4 and 10 centimeters long and the oblique sides are 8 and 12 centimeters long. Fi9nd the angles and the area of the trapezoid

- Pre Calc -
**MathMate**, Monday, October 5, 2009 at 2:53pmThere may be simpler ways of doing, but this is what came to mind for me.

In fact, the problem boils down to finding the height h, and the offset of the two parallel sides, k.

Let ABCD be the vertices of the quadrilateral where AB and DC are parallel sides.

AB=4 centimetres, and

DC=10 centimetres.

Drop a perpendicular from A to the long side DC to intersect at E.

Assume for the moment E is between D and C, so that DEC is a straight line.

Let

k=distance DE, and

h=distance between the two parallel sides = length AE

Consider each of the oblique sides as the hypothenuse of a right triangle,

for ADE,

AE²+DE²=AD²

h²+k²=8² ..... (1)

For the side BC,

(10-k-4)²+h²=BC²

36-12k+k²+h²=144....(2)

Subtract (1) from (2)

36-12k-8²=144

k=-44/12=-11/3

Meaning that the point E is situated on the extension of the line CD.

Substitute k into (1) gives

h=sqrt(8²-(11/3)²)

=sqrt(455)/3

=7.110243

Can you take it from here?

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