Question 1166927
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The two horizontal segments divide triangle ABC into a small triangle, a small trapezoid, and a larger trapezoid.  The heights of all three figures are the same.<br>
Segment BC and the two horizontal segments can also be viewed as forming three similar triangles all with vertex A; the ratio of the heights of those three triangles is 1:2:3.<br>
That means the height of the smallest triangle is 1/3 the height of triangle ABC, so the area of the smallest triangle is 1/9 of the area of triangle ABC.<br>
Similarly, the height of the middle sized triangle is 2/3 the height of triangle ABC, so the area of the middle sized triangle is 4/9 of the area of triangle ABC.<br>
That means the area of the larger trapezoid is 5/9 of the area of triangle ABC.<br>
Finally, since D is the midpoint of BC, segment AD bisects that larger trapezoid, so the area of the figure marked x is 5/18 of the area of triangle ABC.<br>
ANSWER: (5/18)*630 = 5*35 = 175 square cm<br>