In a convex quadrilateral ABCD, the diagonals are halved by the intersection point. From the top of the acute angle

In a convex quadrilateral ABCD, the diagonals are halved by the intersection point. From the top of the acute angle A, the bisector AK is drawn. Find the perimeter of this quadrangle if point K lies on the side BC and BK = 4 cm, and KC = 6 cm.

1. The diagonals of the quadrilateral ABCD are divided by the point of intersection into equal segments. This is one of the hallmarks of a parallelogram. Consequently, the geometric figure given by the condition of the problem is a parallelogram.

2. Bisector BK divides the parallelogram into two geometric shapes. One of them is the isosceles triangle ABK. AB = BK = 4 cm.

3. BC = 4 + 6 = 10 cm.

4. The perimeter of the parallelogram (P) = 2 (AB + BC).

P = 2 x (4 + 10) = 28 cm.

Answer: P is 28 cm.