Show that the areas of the shaded blue triangle and the shaded red triangle are equal.

Find a way of cutting up the blue triangle into some number of pieces and rearranging the pieces to cover the red triangle.

Let the whole triangle be $\Delta ABC$, where $BC$ is divided into three equal parts at points D and E.

So, $BD = DE = EC$

The blue triangle is $\triangle ABD$ and the red triangle is $\triangle AEC$.
Since both triangles have the same height from A to the line BC, their areas are proportional to their bases.

Base of blue triangle = BD

Base of red triangle = EC

But $BD = EC$

Hence, $\text{Area}(\triangle ABD) = \text{Area}(\triangle AEC)$

Therefore, the shaded blue and red triangles have equal areas.

Rearrangement idea

Cut the blue triangle into two pieces by drawing a line from A to the midpoint of BD.

Then:

1. Rotate/slide one piece to the right.

2. Rearrange the two pieces so that together they exactly form the red triangle.

This works because both triangles have equal height, equal base, therefore equal area.