# Parallel to side AB of triangle ABC, a straight line is drawn that intersects side AC at point D so that

Parallel to side AB of triangle ABC, a straight line is drawn that intersects side AC at point D so that AD: DC = 3: 7. Find the area of the trapezoid to be cut if the area of triangle ABC is 200.

1. By the condition of the problem, it is known that a straight line parallel to its base cuts off a smaller triangle from a given triangle.

2. We see that the resulting triangles are similar in the second similarity feature (proportional to the two sides and equal angle between them).

The coefficient of similarity k is determined from the given proportion of the segments AD: DC = 3: 7, which means

k = 7: (7 + 3) = 7/10.

Therefore, both the bases and the heights by which the areas s of the small and S of the large triangles are calculated are in the same proportion, which means that the s of the smaller triangle is 7/10 of 200.

Then we get the area of ​​the trapezoid as the difference S – s = 200 – 200 * 7/10 = 200 – 140 = 60.

Answer: The area of ​​the trapezoid is 60.

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