Question 1150160
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Let the length of the line segment joining the midpoints of the two non-parallel side be x.  Then let the lengths of the two bases be 11-x and 11+x.<br>
The trapezoid has been divided into two trapezoids, in which the ratio of the areas is 4:7.<br>
Let the height of each of those two trapezoids be h (so the height of the original trapezoid was 2h).<br>
The area of a trapezoid is the height, multiplied by the average of the two bases.  Given the ratio of the areas of the two trapezoids is 4:7, we have<br>
{{{(h((11-x+11)/2))/(h((11+11+x)/2)) = 4/7}}}<br>
{{{(22-x)/(22+x) = 4/7}}}
{{{88+4x = 154-7x}}}
{{{11x = 66}}}
{{{x = 6}}}<br>
The lengths of the two parallel sides are 11-x = 5 and 11+x = 17; the product of the lengths of the two parallel sides is 5*17 = 85.<br>