<PRE><B>Question 1148964</B>
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Triangles AMD and CMB are similar.  Since the bases are in the ratio 2:5, their heights are in the ratio 2:5, and their areas are in the ratio 2^2:5^2 = 4:25.&lt;br&gt;
So, given that the area of AMD is 624, we know the area of CMB is 624*(25/4) = 3900.&lt;br&gt;
Triangles AMD and ABD share base AD; and the ratio of their altitudes is 2:(2+5) = 2:7.  So the area of triangle ABD is 624*(7/2) = 2184; and then the area of triangle ABM is 2184-624 = 1560.&lt;br&gt;
By a similar argument, the area of triangle DMC is also 1560.&lt;br&gt;
So the area of the trapezoid is&lt;br&gt;
624+3900+2(1560) = 7644 cm^2.&lt;br&gt;
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Added in response to the reader&#39;s question....&lt;br&gt;
The ratio of similarity between triangles AMD and CMB is 2:5, not 2:7.&lt;br&gt;
2:7 is the ratio of the height of triangle AMD to the height of the trapezoid.&lt;br&gt;
2:7 is also the ratio between the heights of triangles AMD and ABD; and between the heights of triangles AMD and DMC.&lt;br&gt;

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