Hinged seventh
The blue triangle is formed by connecting vertices with points that divide opposite sides in thirds.
The red points are the midpoints of the sides.
When the angle formed by P is zero you have a triangle.
When the angle is 180˚ you have three parallelograms around the blue triangle.
Compare the area of the parallelograms to the area of the blue triangle.
Compare the area of the blue triangle to the big triangle.