In the triangle we have the straight line HE passing through the midpoints of sides AB and AC, and the segment GA perpendicular to this straight line. As the colors indicate, using trapezoid BCEH and triangles AHG and EAG we can construct the rectangle with the same area as the triangle. Intuitively we can see that the parts that make up the triangle also make the rectangle.
If our purpose is to remain inside of the spirit of deductive geometry, we must show that the triangular regions that complete the rectangle obtained from the trapezoid are in fact congruent to the smaller triangles that are part of the original given triangle. To see the demonstration here click