# The area of the triangle ABC is 12. DE is the middle line. Find the area of the triangle CDE.

1. To calculate the area of a triangle, we will use the formula:

S = 1/2 a * h, where a is the base and h is the height of the triangle.

2. By the condition of the problem S ABC = 1/2 * a * h = 12.

It is known that the midline of a triangle is parallel to the base and equal to half of its length, which means that the base of the CDE triangle is equal to 1/2 of the base a.

To determine the height of the triangle CDE, recall Thales’s theorem: if parallel straight lines intersecting the sides of an angle cut off equal segments on one side of it, then equal segments are formed on the other side.

And since the middle line divides the sides of the triangle in half, it also divides the height in half, that is, the height of the CDE triangle is 1/2 * h.

And then S CDE = 1/2 * a / 2 * h / 2 = S ABC: 4 = 12: 4 = 3.

Answer: The area of the triangle CDE is 3.