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

| March 5, 2021 | education

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

Since AE is the bisector of angle A, the angle BAE = DAE.

Angle DАЕ = BEA as cross-lying angles at the intersection of parallel lines AD and BC secant AE. Then the angle BAE = BEA, and the triangle ABE is isosceles and AB = EB = 4 cm.

Since in a parallelogram the opposite sides are equal, then AD = BC = BE + CE = 4 + 2 = 6 cm.

Let’s draw the height of the VN of the parallelepiped. Then, in a right-angled triangle ABN, the VN leg lies opposite the angle 30, and therefore is equal to half the length of the hypotenuse AB. VN = AB / 2 = 4/2 = 2 cm.

Determine the area of ​​the parallelogram.

S = AD * BH = 6 * 2 = 12 cm2.

Answer: The area is 12 cm2.



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