What is the area of a rectangle whose diagonal is 12 cm and the angle between the diagonal

What is the area of a rectangle whose diagonal is 12 cm and the angle between the diagonal and one of the sides is 60 degrees?

In a right-angled triangle ACD, we determine the magnitude of the acute angle CAD.

Angle CAD = 180 – ADC – ACD = 180 – 90 – 60 = 30.

In a right-angled triangle ACD, the CD leg lies opposite angle 30, and therefore its length is equal to half the length of the AC hypotenuse. CD = AC / 2 = 12/2 = 6 cm.

Let us determine the length of the leg AD according to the Pythagorean theorem.

AD ^ 2 = AC ^ 2 – CD ^ 2 = 12 ^ 2 – 6 ^ 2 = 144 – 36 = 108.

АD = 6 * √3 cm.

Determine the area of the rectangle.

Savsd = A * AD = 6 * 6 * √3 = 36 * √3 cm2.

Answer: The area of the parallelogram is 36 * √3 cm2.