The side of the rhombus is 9, and the distance from the center of the rhombus to it is 1. Find the area of the rhombus.

Let’s denote our rhombus ABCD, the diagonals intersect at point O at right angles and the intersection point is divided in half. The diagonals, by their intersection, divide the rhombus into four equal right-angled triangles. Consider one of them, the triangle AOB. The distance from the center to the side of the rhombus OH is the perpendicular, which is the height in this triangle. Let’s find the area of the triangle:
S AOB = 1/2 * a * ha = 1/2 * AB * OH = 1/2 * 9 * 1 = 4.5.
The area of the rhombus is equal to four such areas:
S rhombus = 4 * S triangular. = 4 * 4.5 = 19.
Answer: The area of the rhombus is 19.