The area of an irregular quadrilateral is equal to the length of the connecting line between the midpoints of two adjacent sides of the quadrilateral multiplied by twice the distance from any midpoint of the other two sides to the connecting line.

The quadrilateral obtained by connecting the midpoints of any quadrilateral in turn is called a midpoint quadrilateral, and the midpoint quadrilateral is a parallelogram. The midpoint quadrangle of a diamond is a rectangle, the midpoint quadrangle of a rectangle is a diamond, the midpoint quadrangle of an isosceles trapezoid is a diamond, and the midpoint quadrangle of a square is a square.

Extended data

Classification of quadrangles;

1, convex quadrilateral

The four vertices are in the same plane, the opposite sides do not intersect and are in a straight line with one side, and the other sides are on the same side.

Parallelogram (including: ordinary parallelogram, rectangle, diamond, square).

Trapezoidal (including: common trapezoid, right-angled trapezoid, isosceles trapezoid).

The sum of the inner and outer angles of the convex quadrilateral is 360 degrees. ?

2. Concave quadrilateral

The four vertices of the concave quadrilateral are on the same plane, the opposite sides do not intersect and are in a straight line with one side, and some of the other sides are on different sides.