Question 197372
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Let's begin with the formula for the perimeter of a general quadrilateral, simply the sum of the measures of the four sides, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P = s_1 + s_2 + s_3 + s_4]


We know that the perimeter of this trapezoid is 29 and we know the lengths of 2 of the sides, namely the two non-parallel sides which measure 5 and 4 for a total of 9.  That means that the sum of the measures of the two parallel sides must be 29 - 9 = 20.


Now, let's look at the formula for the area of a trapezoid -- the average of the measures of the two parallel sides times the height.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A = \left(\frac{s_{p1} + s_{p2}}{2}\right)h]


But from our analysis above we know that the sum of the measures of the two parallel sides is 20, regardless what their individual measures are, so just divide 20 by 2 and multiply by the height, 3.  10 times 3 is 30 square units.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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