In parallelogram ABCD, angle D is 30 degrees. Find the area of the parallelogram if the sides are 8 cm and 14 cm.

The first way. The area of a parallelogram is equal to the product of the lengths of its sides by the sine of the angle between them.

Savsd = CD * AD * Sin30 = 8 * 14 * (1/2) = 56 cm2.

Second way.

Let us draw the height of CH, then in a right-angled triangle CDH the leg of CH lies opposite angle 30 and is equal to half the length of the hypotenuse CD. CH = CD / 2 = 8/2 = 4 cm.

Then Savsd = AD * CH = 14 * 4 = 56 cm2.

Answer: The area of the parallelogram is 56 cm2.