The inner triangle

A triangle and two medians. What fraction is shaded?

Scroll down for a solution to this problem.


A fraction of 1/12 is shaded.

It is a known property that the three medians divide the triangle in six equal-area parts. This we have used in the above diagram.

Now using the horizontal side as base and the median from the bottom-left vertex as other side, a triangle is formed which is cut in half by the line segment connecting the midpoints. Therefore A+B=2A-B and hence B=A/2. Since the total triangle has area 6A, the inner triangle is 1/12 of that.

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