What is the area of a rectangle if its diagonal is 18 cm and the angle it forms with the side is equal to 30 degrees.

Let’s draw a diagonal BD.

The AOB triangle is isosceles, since OA = BO = 9 cm, since the diagonals at the intersection point are divided in half.

Angle ОАВ = 90 – CAD = 90 – 30 = 60.

Then triangle AOB is equilateral and angle AOB = 60.

Then Savsd = (1/2) * АС * ВD * SinАВ = (1/2) * 18 * 18 * √3 / 2 = 81 * √3 cm2.

Answer: The area is 81 * √3 cm2.