In parallelogram ABCD, angle B is obtuse. On the extension of side AD beyond the vertex D, point E is marked

In parallelogram ABCD, angle B is obtuse. On the extension of side AD beyond the vertex D, point E is marked so that the angle ECD = 60gr, angle CED = 90gr, AB = 4cm, AD = 10cm find the parallelogram area.

Consider a right-angled triangle DCE, which, by condition, has an angle ECD = 60 and an angle CED = 90, then the angle CDE = 180 – 90 – 60 = 30.

Angle BAD = CDE = 30, as the corresponding angles at the intersection of parallel lines AB and CD of the secant AD.

Determine the area of the parallelogram. Savsd = AB * AD * Sin30 = 4 * 10 * (1/2) = 20 cm2.

Answer: The area of the parallelogram is 20 cm2.