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

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

The area of ​​any figure is equal to the sum of the areas of the figures by which it is divided in some way. The rhombus is divided by its diagonals into four equal right-angled triangles, the hypotenuse of which is the side of the rhombus.

The area of ​​the rhombus will be equal to the sum of the areas of these four triangles.

S = 4S∆.

The area of ​​a triangle is equal to half the product of the base by the height, drawn to the given base. In our case, the base will be the hypotenuse of the triangle, and the height is the distance from the point of intersection of the diagonals of the rhombus to the side of the rhombus, that is, to the hypotenuse.

S∆ = 1/2 * ah;

a = 12, h = 4; S∆ = 1/2 * 12 * 4 = 24.

S = 24 * 4 = 96.

Answer. 96.