Find the area of a rhombus if its perimeter is 80 cm and one of the diagonals is 24.

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

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