Angle A in parallelogram ABCD = 30 degrees, bisector of angle A intersects side BC at point E so BE

Angle A in parallelogram ABCD = 30 degrees, bisector of angle A intersects side BC at point E so BE = 4 and EC = 2 Find the area of this parallelogram

Since, by condition, AE is the bisector of angle A, then the angle BAE = DAE = 150. Angle BEB = DAE, as the angles lying crosswise at the intersection of parallel lines AD and BC secant AE. Then the angle BAE = BEA, and the triangle ABE is equilateral, AB = BE = 4 cm.

Side AD = BC = BE + CE = 4 + 2 = 6 cm.

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

S = AB *AD * Sin30 = 4 * 6 * 1/2 = 12 cm2.

Answer: The area of the parallelogram is 12 cm2.