384 square meters
There is a formula for finding area of a rhombus given diagonal (d) and perimeter (P): 1/4d * √(P² - 4d²), which would be 1/4 * 24 * sqrt (80² - 4*24²), which gives 384
You can break the rhombus up into triangles. In a rhombus the diagonals are perpendicular bisectors of each other, so you have 4 right triangles, and each of them have a side length 12 for one side (since its half of the diagonal). In a rhombus, all sides are equal, so one side is a quarter of the perimeter. This gives a hypotenuse of 20. Using Pythagorean theorem (c² = a² + b²) we get 20² = 12² + x². We get from simplifying that that x² = 256, and x = 16. Since we now have the base and height we can solve for the triangle (bh/2), and we get 12*16/2 = 96. Since that triangle was only a quarter of the rhombus, we multiply by 4 to get the answer of 384
