Determine the area of a rectangle whose diagonal is 24cm and the angle between the diagonals is 60°

Answer 1

The diagonals bisect each other, so you have an isosceles triangle with two sides of length 12 and vertex angle 60°
Thus, the short side of the rectangle is 2*12sin30° = 12
similarly, the long side is 2*12sin60° = 12√3
so the area is 144√3