# Calculate the area of the parallelogram and its diagonal if the sides of the parallelogram are 3√2

**Calculate the area of the parallelogram and its diagonal if the sides of the parallelogram are 3√2 cm, 7 cm, and the angle between these sides is 45 degrees.**

Through the lengths of the sides of the parallelogram and the angle between them, we determine its area.

Savsd = AB * AD * Sin45 = 3 * √2 * 7 * 1 / √2 = 21 cm2.

We define the diagonal ВD using the cosine theorem.

BD ^ 2 = AB ^ 2 + AD ^ 2 – 2 * AB * AD * Cos45 = 18 + 49 – 2 * 3 * √2 * 7 / √2 = 67 – 42 = 25.

BD = 5 cm.

The sum of the adjacent angles of the parallelogram is 180, then the angle ADC = 180 – 45 = 1350.

Then, by the cosine theorem:

AC ^ 2 = AD ^ 2 + CD ^ 2 – 2 * AD * CD * Cos135 = 49 + 18 – 2 * 7 * 3 * √2 * (-1 / √2) = 67 + 42 = 109.

AC = √109 cm.

Answer: The area of the parallelogram is 21 cm2, the diagonals are 25 cm and √109 cm.