The side of the rhombus is 12, and the distance from the point of intersection of the diagonals

The side of the rhombus is 12, and the distance from the point of intersection of the diagonals of the rhombus to it is 4. Find the area of the rhombus.

Given a rhombus ABCD;

The diagonals of the rhombus intersect at point O at right angles and divide the rhombus into 4 equal triangles.

Consider one of the triangles ABO, the height ОD, lowered to the side AB, is equal by condition 4, which means that the area of the triangle is 12 * 4/2 = 24;

The area of the rhombus is 24 * 4 = 96.