What part of the area, counting from the vertex, does the midline of a triangle cut off?

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The cut-off triangle is similar to the given one.

## Solution

First method.

The midline cuts off a triangle similar to the given one with a similarity coefficient of $\frac{1}{2}$. Therefore, its area is $\frac{1}{4}$ of the area of the given triangle.

Second method.

Since the three midlines divide the triangle into four equal triangles, the area of each of them is one-fourth of the area of the given triangle.

![](https://cdn.mathpix.com/cropped/2024_05_06_845c09db4774ba28be39g-18.jpg?height=331&width=666&top_left_y=1744&top_left_x=702)

## Answer

$\frac{1}{4}$