In a rhombus, all sides are equal, so AB = BC = CD = AD = x. The perimeter is the sum of the lengths of all sides, therefore, AB + BC + CD + AD = P; 4x = 80 cm, whence x = 20 cm.
The diagonals of the rhombus at the point of intersection are mutually perpendicular and are divided in half, therefore, BO = BD / 2, and the ABO triangle is rectangular.
We are looking for BО by the Pythagorean theorem from the right-angled triangle ABO.
S (ABCD) = 1/2 * BD * AC; S (ABCD) = 1/2 * 24 * 32 = 384 cm ^ 2
Answer: 384 cm ^ 2
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.